AP Physics B free response practice questions

[Sudhakar_alla]

Homework Statement

two 10-kilogram boxes are connected by a massless string that passes over a massless frictionless pulley. The boxes remain at rest with the one on the right hanging vertically and the one on the left 2.0 meters from the bottom of an inclined plane that makes an angle of 60° with the horizontal. The coefficents of kinetic friction and static friction between the left-hand bax and the plane are 0.15 and 0.30 respectively.

Homework Equations

fk = UkN
N = mg

The Attempt at a Solution

c) Determine the magnitude of the frictional force acting on the box on the plane. The string is then cut and the left-hand box slides down the inclined plane.

D) determine the amount of mechanical energy that is converted into thermal energy during the slide to the bottom.

E) Determine the kinetice energy of the left hand box when it reaches the bottom of the plane.

If someone could explain how they got the answers it would help a lot. Thanks.

 

[ideasrule]

Please show us your attempt solution. Nobody here is going to sit around and explain how to do every question step-by-step unless you've made an honest effort to try the questions yourself.

 

[kerimek]

As a scientist, it is important to have a clear understanding of the concepts and equations being used in a problem, in order to accurately solve it. In this problem, the key concept to understand is the relationship between forces, friction, and energy.

c) To determine the magnitude of the frictional force acting on the box on the plane, we can use the equation for kinetic friction: fk = μkN. In this case, the normal force (N) is equal to the weight of the box, which is mg. Therefore, the frictional force is given by fk = μkmg. Substituting the values given in the problem, we have fk = (0.15)(10 kg)(9.8 m/s^2) = 14.7 N.

d) When the string is cut, the left-hand box will slide down the inclined plane due to the force of gravity. As it slides, some of its mechanical energy will be converted into thermal energy due to friction. We can use the equation for work done by friction, W = μkNΔx, to calculate the amount of mechanical energy converted into thermal energy. In this case, the change in position (Δx) is equal to the length of the inclined plane, which is 2.0 m. Therefore, W = μkmgΔx = (0.15)(10 kg)(9.8 m/s^2)(2.0 m) = 29.4 J.

e) To determine the kinetic energy of the left-hand box when it reaches the bottom of the plane, we can use the equation for kinetic energy, KE = 1/2mv^2. In this case, the mass (m) is 10 kg and the velocity (v) is given by the equation v = √(2gh), where g is the acceleration due to gravity (9.8 m/s^2) and h is the height of the plane (2.0 m). Therefore, v = √(2(9.8 m/s^2)(2.0 m)) = 6.26 m/s. Substituting these values into the equation for kinetic energy, we have KE = 1/2(10 kg)(6.26 m/s)^2 = 196.15 J.