Newton’s Laws Application

Source: Young and Freedman’s University Physics with Modern Physics textbook, 14th edition

Blocks A, B, and C are connected using rope of negligible mass (see figure below). Both A and B weight 23.8 N each, and the coefficient of kinetic friction between each block and the surface is 0.32. Block C descends with constant velocity.

a) Draw free body diagram for blocks A and B.

b) Find tension in rope connecting blocks A and B.

c) What is the weight of block C?

d) If the rope connecting A and B were cut, what would be the acceleration of block C?

Analyze the problem:

The problem has three blocks attached by an inelastic string (so they should have the same acceleration) and pulleys mass ignored. The surface where Blocks A and B are set on have friction and the kinetic friction coefficient was given (kinetic friction coefficient is involved when bodies are in motion which is different than static friction coefficient which used when bodies are not in motion).

What are the given information?

1. Block A weight, FwA=23.8 N
2. Block B weight, FwB=23.8 N
3. Kinetic friction coefficient for all surfaces = 0.32
4. Block C velocity is constant, so acceleration, a =0 m/s2

What are the needed information?

1. Body-diagram draw for blocks A and B.
2. Tension in rope attaching block A and block B.
3. The weight of Block C
4. When rope between block A and block B were cut , then find the acceleration of block C.

SOLUTION:

Note: The acceleration shown in figure below is for part (d).

Two Blocks on Inclined plane

“Physics Principles with Applications”, Douglas C. Giancoli, 7th Edition, Global Edition

44. Two blocks are connected by a light string passing over a pulley of radius 0.15 m and moment of inertia I. The blocks move (toward the right) with an acceleration of 1.00 m/s2 along their frictionless inclines (See figure below). (a) Draw free-body diagrams for each of the two blocks and the pulley. (b) Determine FTA and FTB, the tensions in the two parts of the string. (c) Find the net torque acting on the pulley, and determine its moment of inertia, I.

Analyze the problem:

The problem has two blocks on inclined surfaces and they are attached by an inelastic string (so they should have the same acceleration) the pulley’s mass is not ignored (we know that because the problem mentioned that there is a moment of inertia).

What are the given information?

1. Block A mass, mA=8 kg
2. Block B mass, mB=10 kg
3. Acceleration, a = 1 m/s2
4. Inclination Angle 1, θ1=32º
5. Inclination Angle 2, θ2=61º
6. Radius of pulley, R= 0.15 m

What are the needed information?

1. Body-diagram draw for the two blocks and the pulley.
2. FTA and FTB tension forces
3. The net torque on the pulley
4. The moment of inertia of the pulley

SOLUTION: