Two blocks and of masses and respectively are connected by a light inextensible…

PHYSICS · Subjective · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

Two blocks

A

and

B

of masses

3\,\text{kg}

and

5\,\text{kg}

respectively are connected by a light inextensible string that passes over a small smooth pulley fixed at the top of a rough inclined plane. Block

A

lies on the plane, which is inclined at

30^{\circ}

to the horizontal, while block

B

hangs vertically and is free to move. The coefficient of static friction between block

A

and the plane is

0.40

, and the coefficient of kinetic friction is

0.35

. Take

g = 9.8\,\text{m\,s}^{-2}

. (i) Assuming the system is just on the verge of moving, determine whether the impending motion of block

A

is up the plane or down the plane. (ii) For the direction identified in part (i), derive an expression for the acceleration of the system once motion begins and calculate its magnitude. (iii) Find the tension in the string during the motion. (iv) Determine the range of values of the mass of block

B

for which the system can remain in equilibrium without any motion.

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