Question

Object A ((m_1 = 3 , kg)) is resting on the frictional horizontal surface (the coefficient of kinetic friction is 0.4) and is connected to the second object ((m_2 = 9 , kg)) by an unextendable string passing over a massless pulley. When the hanging block (9 kg) is released from rest, the system starts to move.

a)Find the acceleration of the system.

A. (2.4 , m/s^2)

B. (3.0 , m/s^2)

C. (4.5 , m/s^2)

D. (6.7 , m/s^2)

Answer 1

The acceleration of the system is 2.4 m/s^2.

Step-by-step explanation:

When the hanging block is released, it will accelerate downwards due to the force of gravity. This acceleration will cause the system to start moving, with the blocks moving towards each other.

First, calculate the force of gravity acting on the hanging block using its mass and the acceleration due to gravity (9.8 m/s^2). The force of gravity is given by F = m * g, where m is the mass and g is the acceleration due to gravity.

Next, calculate the frictional force acting on the object on the frictional surface using the coefficient of kinetic friction and the normal force. The frictional force is given by F = μ * N, where μ is the coefficient of kinetic friction and N is the normal force.

Finally, calculate the net force acting on the system by subtracting the force of friction from the force of gravity. Then, divide the net force by the total mass of the system to find the acceleration. Use the equation F = m * a, where F is the net force and m is the total mass of the system.

Using these calculations, the acceleration of the system is found to be 2.4 m/s^2 (option A).