Two blocks connected by a string are pulled across a horizontal surface by a force applied to one of the blocks,as shown.The coefficient of kinetic friction between the blocks and the surface is 0.25.If each block has an acceleration of 2.0 m/s² to the right,what is the magnitude F of the applied force? A)25 N B)18 N C)11 N D)14 N E)7.0 N

Question

Quizplus · Accepted Answer

The force applied on the system is equal to the force of friction acting on the blocks, since the acceleration of the blocks is given and there is no other external force acting on the system.

Using Newton's second law: 
F_applied - F_friction = (m1 + m2) * a

where F_friction = (m1 + m2) * g * mu_k

F_applied - (m1 + m2) * g * mu_k = (m1 + m2) * a

Substituting values: 
F_applied - 0.25 * (m1 + m2) * g = (m1 + m2) * 2

F_applied - 0.25 * (2 + 1) * 9.81 = 3 * 2 
F_applied - 7.3575 = 6 
F_applied = 6 + 7.3575 
F_applied = 13.3575 N

Therefore, the magnitude of the applied force is approximately 25 N.

Two Blocks Connected by a String Are Pulled Across a Horizontal