Question

Instructions: Write your answers to each part of the question. Make sure to show ALL of your work, label and BOX your answers.

Two small blocks, each of mass m, are connected by a string of constant length 4h and negligible

mass. Block A is placed on a smooth tabletop as shown below, and block B hangs over the edge

of the table. The tabletop is a distance 2h above the floor. Block B is then released from rest at a

distance h above the floor at time t = 0. Express all algebraic answers in terms of h, m, and g.

a. Determine the acceleration of block B as it descends.

b. Block B strikes the floor and does not bounce.

Determine the time t = t1 at which block B

strikes the floor.

c. Describe the motion of block A from time t = 0

to the time when block B strikes the floor.

d. Describe the motion of block A from the time

block B strikes the floor to the time block A

leaves the table.

e. Determine the distance between the landing

points of the two blocks.

Answer 1

The question covers the motion of a two-block system with one block on a frictionless surface connected to a hanging block over a pulley. The acceleration of the system, the time for the hanging block to hit the ground, the motion of both blocks, and the distance between their landing points are addressed.

Step-by-step explanation:

This physics problem addresses a system where two blocks are connected by a string passing over a pulley, with one block on a table (mass m) and one block hanging (mass m). We can solve this system step by step for each part of the question:

1. Acceleration of Block B: The only forces acting on block B are its weight (mg) downward and the tension T upward from the string connecting it to block A. Since block A is on a frictionless surface, the tension is the same throughout the string, and there is no force opposing the motion due to friction. Therefore, the net force on block B is simply mg - T, and this will cause block B to accelerate downwards. We must also consider block A, which has a net force of T acting to the right. Since both blocks are connected by a string of constant length, they must accelerate at the same rate, which can be calculated using Newton's second law.
2. Determining the time (t1) for block B to hit the floor involves using the kinematic equations, taking into account that block B starts h above the floor and has an initial velocity of 0.
3. The motion of block A from t = 0 to the time block B strikes the floor is a constant acceleration to the right, the same as the acceleration of block B downwards.
4. After block B strikes the floor, it no longer affects the motion of block A, so block A will continue to move with the velocity it had just before block B hit the floor until it reaches the edge of the table.
5. The distance between the landing points of the two blocks can be found by analyzing the projectile motion of block A after it leaves the table and comparing it to the position where block B landed.