Pulley and friction problem

• AcecA
In summary, the problem involves a 100-lb block A moving down a plane at 5 ft/s while attached to a 50-lb block B. The coefficient of friction is 0.2 and the mass of the pulleys and cables is neglected. The goal is to determine the acceleration of A and the distance it slides before stopping. The frictional force of block A is found to be 16-lb and the tension force in the rope at A is calculated to be 12.5-lb. However, to accurately solve the problem, the normal force must first be found, which depends on the acceleration. Using Newton's second law for both blocks, the correct values for acceleration and distance are found to be
AcecA

Homework Statement

At the instant shown the 100-lb block A is moving down the plane at 5 ft/s while being attached to the 50-lb block B. If the coefficient of friction is µk = 0.2, determine the acceleration of A and the distance A slides before it stops. Neglect the mass of the pulleys and cables.
http://0pcode.ath.cx/photo.jpg
The picture was taken with my phone, so the triangle under A is kinda hard to see. Its hypoteneuse is 5, the vertical leg is 3, and the horizontal leg is 4.

Homework Equations

F = ma
m = W/g (slug)
F(friction) = µ*N
V$$^{2}$$ = V$$^{2}_{0}$$ + 2ad

The Attempt at a Solution

I tried finding the frictional force of block A first, which I calculated to be 16-lb. I then found the tension force in the rope at A, which I calculated to be 12.5-lb. I then took those two values and added them together, and got an acceleration value of 9.12ft/s^2. And I found the distance the block slides to be 1.37 feet.
The answers are supposed to be 1.29ft/s^2, and 9.70 feet. I don't know where I went wrong, any help would be appreciated :) Thanks.

Last edited by a moderator:
Hi AcecA!
AcecA said:
… I tried finding the frictional force of block A first, which I calculated to be 16-lb. I then found the tension force in the rope at A …

Nooo … to find the friction force, you first need to find the normal force, and that will depend on the acceleration.

In this sort of problem, everything depends on everything else

you can't "start at one end and work your way across" (the way we do in most mechanics problems )

Hint: call the tensions T1 and T2, and the distance along the slope x, and then use good ol' Newton's second law twice, once for A and once for B.

I would like to point out that there seems to be some confusion in the given problem. The values provided for the hypotenuse and the vertical leg of the triangle do not match the given information of the block A's motion. Additionally, the given values for the friction coefficient and the mass of the blocks do not align with the calculated values.

Assuming that the given values are correct, I would suggest double-checking your calculations and equations. It is also important to consider the direction of the forces and the motion of the blocks. The block A is moving down the plane, which means the friction force will act in the opposite direction. The tension in the rope should also be considered in the equation for block A's acceleration.

Furthermore, it is important to consider the pulley and cable system in the problem. The mass of the pulleys and cables should also be taken into account, as they will affect the overall motion and acceleration of the blocks.

In conclusion, it is important to carefully analyze the given problem and consider all the relevant factors in order to accurately solve the problem. Double-checking calculations and equations is also crucial in order to avoid errors.

1. What is a pulley and friction problem?

A pulley and friction problem is a type of physics problem that involves using pulleys and the concept of friction to determine the motion and forces of objects in a system. This type of problem is commonly used in engineering and mechanics to understand how machines and systems work.

2. How do you solve a pulley and friction problem?

To solve a pulley and friction problem, you first need to draw a diagram of the system and label all the forces acting on the objects. Then, you can use Newton's laws of motion and equations for friction to determine the forces and acceleration of the objects. It may also be helpful to use vector diagrams and free-body diagrams to visualize the forces at play.

3. What is the difference between static and kinetic friction in a pulley and friction problem?

Static friction is the force that prevents two surfaces from sliding past each other when there is no motion. In a pulley and friction problem, static friction can be used to determine the minimum force needed to move an object. Kinetic friction, on the other hand, is the force that opposes the motion of objects that are already moving. It is typically smaller than static friction and is used to calculate the acceleration of objects in a system.

4. How do pulleys affect the forces in a pulley and friction problem?

Pulleys can change the direction and magnitude of forces in a pulley and friction problem. By using multiple pulleys, the amount of force needed to lift an object can be reduced, but the distance the force needs to act over is increased. This allows for easier lifting of heavy objects. Additionally, the friction between the pulley and the rope can also affect the forces in a pulley system.

5. What real-life applications use pulleys and friction?

Pulleys and friction are used in many real-life applications, including elevators, cranes, and escalators. Pulleys are also commonly used in weightlifting machines and exercise equipment. In engineering and industry, pulleys and friction are used in conveyor belts, winches, and other machinery. Understanding how these concepts work together is essential for designing and maintaining efficient and effective systems.

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