Determine the magnitude of the resultant force acting on the pin
Answers
To determine the magnitude of the resultant force acting on the pin, the following steps should be followed as the magnitude of the resultant force is the vector sum of all the individual forces acting on the object or the system.
1. Draw a vector diagram of the forces acting on the object or system, with each force represented by an arrow. The length of each arrow should be proportional to the magnitude of the force, and the direction of each arrow should indicate the direction of the force.
2. Identify all the individual forces acting on the pin.
3. Break down each force into its horizontal and vertical components (if necessary).
4. Sum up all the horizontal components to find the total horizontal force.
5. Sum up all the vertical components to find the total vertical force.
6. Use the Pythagorean theorem to find the magnitude of the resultant force: Resultant force = √(total horizontal force² + total vertical force²).
7. If we have two or three forces acting on an object or system, we can use vector addition to determine the magnitude and direction of the resultant force.
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Related Questions
We have a program with 30 billion instructions that takes 45 seconds to run on a 2GHz machine. It is given that the program consists of 25% branch instructions, and the CPI of branch instructions is 4. The average CPI is 3.0.
Using a newly developed compiler, the recompiled program now uses 20 billion instructions. It is still composed 25% branch instructions, but the CPI of the branch instructions has been reduced by a factor of 2. What is the expected speedup of the new program over the original program?
Answers
The expected speedup of the new program over the original program is approximately 2.25 times faster. This means that the recompiled program is expected to run in approximately 20 seconds, compared to the original program's runtime of 45 seconds. The original program has 30 billion instructions and an average CPI of 3.0.
This gives us the total number of cycles required to execute the program as (30 billion instructions) x (3.0 CPI) = 90 billion cycles. Since the machine has a clock rate of 2 GHz, the time taken to execute the program is (90 billion cycles) / (2 GHz) = 45 seconds.
In the recompiled program, the number of instructions has been reduced to 20 billion, while still maintaining a 25% branch instruction composition. The CPI of the branch instructions has been reduced by a factor of 2, which means the new CPI is 4 / 2 = 2.0. Using the same calculation, the total number of cycles required to execute the recompiled program is (20 billion instructions) x (2.0 CPI) = 40 billion cycles. With the same clock rate of 2 GHz, the expected runtime of the recompiled program is (40 billion cycles) / (2 GHz) = 20 seconds.
Comparing the runtimes of the original and recompiled programs, we can calculate the speedup as (original runtime) / (recompiled runtime) = 45 seconds / 20 seconds ≈ 2.25. Therefore, the expected speedup of the new program over the original program is approximately 2.25 times faster.
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The expected speedup of the new program over the original program is 1.8x.
1. Calculate the total number of branch instructions in the original program:
Total branch instructions = 30 billion instructions * 25% = 7.5 billion instructions
2. Calculate the total number of non-branch instructions in the original program:
Total non-branch instructions = 30 billion instructions - 7.5 billion instructions = 22.5 billion instructions
3. Calculate the average CPI of the original program:
Average CPI = (CPI of branch instructions * percentage of branch instructions) + (CPI of non-branch instructions * percentage of non-branch instructions)
Average CPI = (4 * 25%) + (1 * 75%) = 1 + 0.75 = 1.75
4. Calculate the execution time of the original program:
Execution time = Total instructions / (Clock rate * CPI)
Execution time = 30 billion instructions / (2 GHz * 1.75) = 8.5714 seconds
5. Calculate the total number of branch instructions in the recompiled program:
Total branch instructions = 20 billion instructions * 25% = 5 billion instructions
6. Calculate the total number of non-branch instructions in the recompiled program:
Total non-branch instructions = 20 billion instructions - 5 billion instructions = 15 billion instructions
7. Calculate the CPI of the branch instructions in the recompiled program:
CPI of branch instructions = CPI of original branch instructions / Reduction factor = 4 / 2 = 2
8. Calculate the average CPI of the recompiled program:
Average CPI = (CPI of branch instructions * percentage of branch instructions) + (CPI of non-branch instructions * percentage of non-branch instructions)
Average CPI = (2 * 25%) + (1 * 75%) = 0.5 + 0.75 = 1.25
9. Calculate the execution time of the recompiled program:
Execution time = Total instructions / (Clock rate * CPI)
Execution time = 20 billion instructions / (2 GHz * 1.25) = 8 seconds
10. Calculate the expected speedup of the new program over the original program:
Speedup = Execution time of original program / Execution time of new program
Speedup = 8.5714 seconds / 8 seconds = 1.0714
11. Round the speedup value to two decimal places:
Speedup = 1.07
Therefore, the expected speedup of the new program over the original program is 1.8x.
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In a high-quality coaxial cable, the power drops by a factor of 10 approximately every 5 km. If the original signal power is 0.25 W (=2.5 x 10-1), how far will a signal be transmitted before the power is attenuated to 25 μW? As part of your answer, include a Table showing the signal power vs. distance in 5 km intervals. If optical fibre is used instead of the coaxial cable, briefly explain how you would expect the above calculated distance value to change. You are not required to include another Table.
Answers
Answer:
20 km for 40 dB loss80 km for 40 dB loss, or 10 dB loss for 20 kmExplanation:
Here's your table of (distance, power level):
(0 km, 250 mW), (5 km, 25 mW), (10 km, 2.5 mW),
(15 km, 250 μW), (20 km, 25 μW)
The signal can be transmitted 20 km before being attenuated to 25 μW.
__
Reportedly, the loss in fiber optic cable is about 0.5 dB/km. This compares to 10 dB/5 km = 2 dB/km for the coaxial cable. Loss in dB/km is a factor of 4 less for fiber optic cable, so the distance for the same loss would be multiplied by 4.
No help dude that’s not even part of the question
Answers
Answer:
wat?
Explanation:
The question should be labeled in the psychology section, but what I assume the question means is some sort of paradoxical reverse psychology method of braincell loss. Even photosynthesis doesn't understand what it means. The question probably is what is the question, not that there's no help.
Hope this helps (a little)!
What is the single largest contributor to increasing takeoff or landing distance?
Answers
An uphill slope improves the take-off ground run, and a downhill slope increases the landing ground run.
What is uphill slope?
Driving uphill suggests climbing a “positive” six percent slope . Driving downhill, the “rise” exists as a drop, so there is a “negative,” or downhill, slope (Figure B). When dealing with slope, a positive slope simply indicates uphill and a negative slope indicates downhill. An uphill slope improves the take-off ground run, and a downhill slope increases the landing ground run.
If something or someone lives moving downhill or is downhill, they exist moving down a slope or are located toward the bottom of a hill. He headed downhill toward the river. adverb. If you communicate that something exists going downhill, you mean that it is becoming worse or less prosperous.
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Compare automation and autonomous
Answers
Answer:
Automation generally means “a process performed without human assistance”, while autonomy implies “satisfactory performance under significant uncertainties in the environment and the ability to compensate for system failures without external intervention [emphasis mine].”
Explanation:
what's better than a trophy truck and an ultra 4
Answers
Answer:
A ultra 4. that would be amazing to have that.
Answer:
I have know idea
Explanation:
For communication channel using optical fibre sending multiple frames of 1000 bits at a
data rate of 1 Mbps between two nodes 2000km apart calculate the efficiency of stop and
wait? Sketch a picture of the transmission.
Answers
To calculate the efficiency of stop and wait protocol we can use the formula:
Efficiency= $\frac{Frame size}{Frame size + 2 \times Delay}$
To calculate the delay, we can use the following formula:
Delay = $\frac{Distance}{Propagation speed}$
The propagation speed for an optical fiber is 2 × 10^8 m/s.
Therefore, the delay will be:
Delay = $\frac{2000 \times 1000}{2 \times 10^8}$ = 0.01 sec
Now that we have calculated the delay, let's use this value to calculate the efficiency of stop and wait protocol.
Efficiency = $\frac{1000}{1000 + 2 \times 0.01 \times 1 \times 10^6}$
Efficiency = 49.875 %
Thus, the efficiency of stop and wait protocol is 49.875 %.
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Question 1 Conduct a risk assessment for the following tasks performed on ships: - Cleaning liquid cargo spilled from a container carrying dangerous goods (Class 5). - Entering confined space to rescue an injured crew member (sprained ankle). The students should: i) Identify all associated risks ii) Classify the risks under the following risk estimation framework: iii) Develop strategies to mitigate the identified risks. No word limit. [20 Marks]
Answers
Identify risks: Cleaning hazardous liquid spills (medium likelihood, major severity), confined space rescue (high likelihood, moderate severity). Mitigate risks with PPE, training, protocols, and proper ventilation.
Step 1: Identify all associated risks:
a) Cleaning liquid cargo spilled from a container carrying dangerous goods (Class 5):
- Exposure to hazardous chemicals or substances in the spilled cargo.
- Risk of chemical burns or respiratory problems due to inhalation or contact with the dangerous goods.
- Slippery surfaces leading to falls and injuries.
- Fire or explosion risks if the spilled cargo is flammable or reactive.
b) Entering confined space to rescue an injured crew member (sprained ankle):
- Lack of oxygen or presence of toxic gases in the confined space.
- Risk of physical injuries due to confined space hazards such as uneven surfaces, low visibility, or falling objects.
- Difficulty in accessing and rescuing the crew member due to limited space.
Step 2: Classify the risks under the risk estimation framework:
The risk estimation framework can vary, but a commonly used approach is to assess risks based on their likelihood and severity. For each identified risk, assign a rating for likelihood (e.g., low, medium, high) and severity (e.g., minor, moderate, major).
Example:
- Cleaning liquid cargo spilled from a container carrying dangerous goods:
- Likelihood: Medium
- Severity: Major
- Entering confined space to rescue an injured crew member:
- Likelihood: High
- Severity: Moderate
Step 3: Develop strategies to mitigate the identified risks:
a) Cleaning liquid cargo spilled from a container carrying dangerous goods:
- Provide appropriate personal protective equipment (PPE) to workers involved in the cleanup.
- Train workers on proper handling and disposal procedures for hazardous materials.
- Implement spill containment measures and cleanup protocols.
- Conduct regular inspections and maintenance of containers to minimize the risk of spills.
b) Entering confined space to rescue an injured crew member:
- Assess the confined space for hazardous conditions and ensure proper ventilation before entry.
- Use a buddy system and have a standby person outside the confined space for communication and assistance.
- Equip the rescue team with appropriate PPE, including gas detectors, harnesses, and rescue equipment.
- Establish emergency response procedures and provide training to crew members on confined space rescue techniques.
It is important to note that risk assessment should be conducted by qualified professionals who have expertise in ship operations and safety regulations. The strategies mentioned above are general recommendations and may need to be tailored based on specific ship and task requirements. Regular reviews and updates of risk assessments should be conducted to ensure ongoing safety and compliance.
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The water level in a tank z1, is 16 m above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The tank cover is airtight, and the air pressure above the water surface is 2 atm gage. The system is at sea level. Determine the maximum height to which the water stream could rise. Take the density of water to be 1000 kg/m3.
Answers
Answer:
40.7 m
Explanation:
Let point 1 represent the surface of the water, point 2 be the top of the water trajectory and the reference be the bottom of the tank. Hence:
\(z_1=16\ m,P_1=2\ atm,V_1=0(velocity\ at\ the \ surface \ of\ water\ is\ low)\\V_2=0,P_2=P\\\\Using\ Bernoulli\ equation:\\\\\frac{P_1}{\rho g} +\frac{V_1^2}{2g}+z_1= \frac{P_2}{\rho g} +\frac{V_2^2}{2g}+z_2\\\\Sine\ V_1=0,V_2=0:\\\\\frac{P_1}{\rho g} +z_1=\frac{P}{\rho g} +z_2\\\\z_2=\frac{P_1}{\rho g} -\frac{P}{\rho g} +z_1\\\\z_2=\frac{P_1-P}{\rho g} +z_1\\\\z_2=\frac{P_{1.gage}}{\rho g} +z_1\\\\\)
\(z_2=\frac{2\ atm}{1000\ kg/m^3*9.81\ m/s^2}(\frac{101325\ N/m^2}{1\ atm} )(\frac{1\ kg.m/s^2}{1 \ N} ) +20\\\\z_2=20.7+20\\\\z_2=40.7\ m\)
Write a procedure that produces N values in the Fibonacci number series and stores them in an array of doubleword then display the array to present Fibonacci numbers in hexadecimal (calling the DumpMem method from the Irvine32 library). Input parameters should be a pointer to an array of doubleword, a counter of the number of values to generate. Write a test program that calls your procedure, passing N = 30. The first value in the array will be 1, and the last value will be 832040 (000CB228 h)
Answers
The Fibonacci series is a sequence of numbers that starts with 0 and 1, and each subsequent number is the sum of the previous two numbers. In this question, we are supposed to write a procedure that produces N values in the Fibonacci number series.
Stores them in an array of doubleword and then display the array to present Fibonacci numbers in hexadecimal (calling the Dump Mem method from the Irvine32 library).The above code declares an array named arr of 30 doublewords.
It then calls the Fibonacci procedure and passes the address of the array and the length of the array as parameters. Finally, it displays the array in hexadecimal using the DumpMem method from the Irvine32 library.
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All of the following are advantages of using a pressure transducer rather than a vacuum gauge EXCEPT:
Answers
Question:
All of the following are advantages of using a pressure transducer rather than a vacuum gauge EXCEPT:
A. greater accuracy.
B. easier identification of the cylinder.
C. measuring higher pressures.
D. ability to see the levels graphically
Answer:
The correct answer is D) ability to see the levels graphically
Explanation:
The above question derives from the Rudiments of Automotive Technology.
The function of the pressure transducer is to enable the diagnostic who is testing the engine vacuum to detect the cylinder with a faulty vacuum.
The pressure transducer does allow its user to see the vacuum graphically NOT the levels.
Cheers.
design process 8 steps with definition
Answers
Answer:
Step 1: Define the Problem.
Step 2: Do Background Research. .
Step 3: Specify Requirements. .
Step 4: Brainstorm, Evaluate and Choose Solution.
Step 5: Develop and Prototype Solution.
Step 6: Test Solution.
Step 7: Does Your Solution Meet the Requirements?
Step 8: Communicate Results.
can u tell me the definition tho?
palled correctly as “though” which is an alternate form of “although”) at the end is informal usage. It's better placed before “she seems better today
2.2.2 Make a list of the electronic components that could be used in making this product (energy saving switch).
Answers
The electronic components that could be used in making of energy saving switch are:
Transistors semiconductor devices CapacitorsCoils (inductors) Which electronic component is used as a switch?Transistors as well as other kinds of semiconductor devices are known to be tools or element that can be used in the making of switches. In its use or applications.
Note that the base or gate of a transistor, based on the kind of transistor that is known to be in use, and it is one that is often employed as a form of control element to be able to switch on as well as switch off the current that often exist between the emitter as well as the collector or the source and that of the drain.
Note also that the electronic components that are able to store energy in regards to electronic devices, are known to be capacitors and coils (inductors) and they often play a key function of temporarily saving energy. One key role of a capacitor is to save an electric charge.
Therefore, The electronic components that could be used in making of energy saving switch are:
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A pointer is spun on a fair wheel of chance having its periphery labeled Trom 0 to 100. (a) Whhat is the sample space for this experiment? (b)What is the probability that the pointer will stop between 20 and 35? (c) What is the probability that the wheel will stop on 58?
Answers
Answer:
A pointer is spun on a fair wheel of chance having its periphery labeled Trom 0 to 100. (a) Whhat is the sample space for this experiment? (b)What is the probability that the pointer will stop between 20 and 35? (c) What is the probability that the wheel will stop on 58?
Explanation:
thats all you said
Answer:
hii my name is RAGHAV what is your name
Explanation:
this question is which chapter
I need this word meaning and definition need asap?
Answers
Answer:
1. Alleviate: to make pain/suffering less severe.
2. Strenuous: requiring much energy and effort.
3. Revolutionize: to overthrow the established government; to change fundamentally.
4. Repetitive: doing or saying the same thing multiple times.
5. Prosthetics: a device designed to replace a missing body part, or make a part work better.
6. Infrastructure: the fundamental facilities and systems serving a country, city, or another area, including the services and facilities necessary for its economy to function.
a. kmods
b. modinfo
c. mod_info
d. modules
Answers
When processing a module, the computer leaps to it, runs its instructions, and then moves on to the next executable command.
The program jumps to the module, runs its instructions, and then moves on to the following executable instruction. The term "software development life cycle" (SDLC) refers to a strategic technique or process that outlines the essential processes or phases for designing and putting into practice high-quality software applications. One or more repetitive functions can be found in a module, which is a discrete software component or unit of a hardware program (tasks Through a programming interface, a module can be utilized in a variety of software programs or computer systems since it is portable. Additionally, they are interoperable since they typically work with different parts of a system or software application.
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SAHARA
Jeep
WRANGLES
G
Answers
Answer:
lol what
smmsdnndnsnsnnd
which type of clectrical circuit is represented by this diagram?
Answers
Answer:
parallel
Explanation:
All components in this circuit are tied in parallel. Each component experiences the same voltage from one terminal to the other. It is a parallel circuit.
A company wants to develop audio speakers using an inexpensive type of plastic that has a very high quality of sound output. Which customers would most likely give a high evaluation of this product?
Answers
Answer:A
Explanation:
Those who want to save money and will use the product for only a few years
Answer:
THE ANSWER is A - those who want to save money and will use the product for only a few years
Explanation: Got it right on edg 2021
Imagine you are a process safety consultant and you have been tasked to make a metal refinery site DSEAR compliant. What are the steps you will take to complete this task? Justify your answer.
Answers
Complying with DSEAR involves:
Assessing risks. ...
Preventing or controlling risks. ...
Control measures. ...
Mitigation. ...
Preparing emergency plans and procedures. ...
Providing information, instruction and training for employees. ...
Places where explosive atmospheres may occur ('ATEX' requirements)
hse uk
QUESTION 4
D
Which of the four strokes of a four-cycle internal combustion engine is the shortest in crankshaft duration?
O A.Power
O b.Exhaust
O c. Intake
O d. Compression
Answers
Answer:
The answer will be B i hope this helps
please i want to paraphrase this paragraph please helppppppppp don't skip!!!!!!
Answers
FAT ASE 6 Electrical - (F
When probing wires, you should do all these, EXCEPT:
Select one:
a. back probe when possible.
O b. use very fine pins to reduce the possibility of damage.
O c. reinsulate the hole with room temperature vulcanizing (RTV) silicone.
RTV)
O d. always reinsulate the hole that the probe makes to prevent any corrosion.
Clear my choice
Answers
Answer:
The answer is: c. reinsulate the hole with room temperature vulcanizing (RTV) silicone.
Which of the following is false about most machine learning models?
They require numbers or collections of numbers as input.
They are flexible enough to handle all issues you might see in your dataset (lack of data, incorrect data, etc)
They are trained by iteratively adjusting their parameters to minimize a loss function.
Once trained, their model parameters can be used to make new predictions in a process called a “model inference algorithm.”
Answers
The false statement about most machine learning models is that: B. they are flexible enough to handle all issues you might see in your dataset (lack of data, incorrect data, etc).
What is machine learning?Machine learning (ML) is also referred to as deep learning or artificial intelligence (AI) and it can be defined as a subfield in computer science which is typically focused on the use of data-driven techniques (methods), computer algorithms, and technologies to develop a smart computer-controlled robot with an ability to automatically perform and manage tasks that are exclusively meant for humans or solved by using human intelligence.
Generally speaking, machine learning models are designed and developed to accept numerical data (numbers) or collections of numerical data (numbers) as an input.
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You have been asked to participate as an “Engineer in Training” in the design and construction of a nuclear power plant. You will be working in a team of 10 design engineers. Some of the engineers are experienced and capable nuclear plant designers.
a) Is the use and development of nuclear power plant ethical? Explain(5 marks)
b) Can you participate in the design of such a plant without any previous experience?(5 marks)
Answers
a. Yes, because you will be working in a team of 10 design engineers and take note some of them are experienced and capable nuclear plant designers.And from what i have learn about engineers, they can't be called engineers for nothing.All you have to do is trust yourself and your team.
b.Of course i cannot but because i have my team (10 design engineers) i know i can do a great job and they are experienced in this stuff so i am confident that i can participate and can make a good job and even if i do not have any experience i know i will learn from them.I can call this assignment as my experience right?
Nuclear power plants uses nuclear fuels as a source of energy.
A nuclear power plant is a power generating plant that makes use of nuclear fuels as a source of energy for power generation. This means of power generation has the advantage that 1 g of nuclear fuel can be used for several years.
On the downside, this means of power generation is prone to hazards such as nuclear explosions and radioactive fallout. This means of power generation is ethical as long as all the safety standards are followed.
I can participate in such a design as a trainee engineer without any previous experience because participating in such project is a huge learning opportunity for me.
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What is the minimal set of MIPS instructions that may be used to implement the following pseudoinstruction, not $ut, $t2 il bit-wise invert O nor $11. $12. St2 O nor St2, $t1, $11 O nori $t1. $12. $12 O nor $t1,$t1, $t2
Answers
We can decompose the supplied pseudoinstruction into smaller parts and implement it with a minimal set of MIPS instructions.
Here is one conceivable application:
Use the XORI (exclusive OR immediate) instruction and the immediate value -1 to perform bit-wise inversion (not operation) on register $t2:
XORI $t2, $t2, -1
The NOR instruction can be used to carry out the following operation between registers $11 and $12 and save the outcome in $t2:
NOR $t2, $11, $12
With the assumption that $t1 holds the memory address, we can use the SW (store word) instruction to store the output of NOR into memory at address $t1:
SW $t2, 0($t1)
The NORI (NOR instant) instruction can be used to execute a NOR operation between the value in $t1 and the immediate value -12 and store the outcome in $12:
NORI $12, $t1, -12
The NOR instruction can be used to execute a NOR operation between the values in $t1 and $t2 and then store the outcome back in $t1:
NOR $t1, $t1, $t2
Thus, the bare minimum set of MIPS instructions required to execute the provided pseudoinstruction is shown here.
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difference between PN junction diode and Bipolar diodes?
Answers
PN junction diode and bipolar junction diode are two types of diodes with distinct characteristics and functionalities.
A PN junction diode is a semiconductor device formed by the junction of a p-type region and an n-type region. It operates based on the principle of a PN junction's rectifying behavior, allowing current flow in only one direction. When a forward bias is applied, the diode conducts current, while in reverse bias, it acts as an insulator. PN junction diodes are commonly used for rectification and signal demodulation in electronic circuits.On the other hand, a bipolar junction diode (BJT) consists of three regions: the emitter, base, and collector. It functions as a current-controlled device and can operate in two modes: NPN (negative-positive-negative) and PNP (positive-negative-positive). BJTs are known for their ability to amplify signals and are widely used in applications such as amplifiers, switches, and digital logic circuits.In summary, the main difference between PN junction diode and bipolar junction diode lies in their construction and operating principles. PN junction diodes are based on a single PN junction and primarily used for rectification, while bipolar junction diodes are composed of multiple regions and employed for signal amplification and switching.
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in a distributor ignition system, what rotates under the distributor cap to send the high voltage to each spark plug wire?
Answers
In a distributor ignition system, the rotor rotates under the distributor cap to send the high voltage to each spark plug wire.
The rotor is a small, cylindrical component that is typically made of plastic with a conductive metal tip on the end. It is attached to the distributor shaft and rotates at the same speed as the engine's crankshaft. As the rotor rotates, it passes over a series of metal contacts, known as the distributor cap terminals, which are connected to the spark plug wires. When the rotor passes over a terminal, it completes the circuit and sends a high voltage pulse to the corresponding spark plug wire, which ignites the fuel in the engine's cylinders.
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if a plcs input indicators are correct but expected outputs are not produced what is the first step to troubleshoot the problem
Answers
The first step to troubleshoot the problem is: If a PLC's input indicators are correct but expected outputs are not produced, the first step to troubleshoot the problem is to check the program or ladder logic to see if it is correct.
A programmable logic controller (PLC) is an industrial computer system that is designed to perform automation functions, particularly for controlling and managing manufacturing processes. The main function of a PLC is to monitor inputs and control outputs to perform a specified operation based on the programmed logic. PLCs are used to perform different functions, such as controlling various motors, pumps, valves, and sensors.The following are the steps to troubleshoot the problem if a PLC's input indicators are correct but expected outputs are not produced:Check the program or ladder logic to see if it is correctCheck the wiring between the output module and the device that the PLC is supposed to control.
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A horizontal force P is applied to a 130 kN box resting on a 33 incline. The line of action of P passes through the center of gravity of the box. The box is 5m wide x 5m tall, and the coefficient of static friction between the box and the surface is u=0.15. Determine the smallest magnitude of the force P that will cause the box to slip or tip first. Specify what will happen first, slipping or tipping.
Answers
Answer:
SECTION LEARNING OBJECTIVES
By the end of this section, you will be able to do the following:
Distinguish between static friction and kinetic friction
Solve problems involving inclined planes
Section Key Terms
kinetic friction static friction
Static Friction and Kinetic Friction
Recall from the previous chapter that friction is a force that opposes motion, and is around us all the time. Friction allows us to move, which you have discovered if you have ever tried to walk on ice.
There are different types of friction—kinetic and static. Kinetic friction acts on an object in motion, while static friction acts on an object or system at rest. The maximum static friction is usually greater than the kinetic friction between the objects.
Imagine, for example, trying to slide a heavy crate across a concrete floor. You may push harder and harder on the crate and not move it at all. This means that the static friction responds to what you do—it increases to be equal to and in the opposite direction of your push. But if you finally push hard enough, the crate seems to slip suddenly and starts to move. Once in motion, it is easier to keep it in motion than it was to get it started because the kinetic friction force is less than the static friction force. If you were to add mass to the crate, (for example, by placing a box on top of it) you would need to push even harder to get it started and also to keep it moving. If, on the other hand, you oiled the concrete you would find it easier to get the crate started and keep it going.
Figure 5.33 shows how friction occurs at the interface between two objects. Magnifying these surfaces shows that they are rough on the microscopic level. So when you push to get an object moving (in this case, a crate), you must raise the object until it can skip along with just the tips of the surface hitting, break off the points, or do both. The harder the surfaces are pushed together (such as if another box is placed on the crate), the more force is needed to move them.