Question

A block with mass m1 = 5 kg and another block with mass m2 = 8 kg are connected by a light string that passes over a pulley. The block with mass m1 is located on a table, while the block with mass m2 is hanging off the side of the table. Both the string and pulley are massless. The coefficient of kinetic friction between the block with mass m1 and the table is measured to be 0.2. (a) Find the acceleration of the two objects and the tension in the string.

Answer 1

To find the acceleration of the two objects and the tension in the string, we can apply Newton's laws of motion. Let's call the acceleration of the system 'a' and the tension in the string 'T'. The acceleration of the system is 1.68 m/s² and the tension in the string is 11.52 N.

Step-by-step explanation:

To find the acceleration of the two objects and the tension in the string, we can apply Newton's laws of motion. Let's call the acceleration of the system 'a' and the tension in the string 'T'.

1. Calculate the net force acting on the block on the table:

• The weight of the block on the table is m1 * g, where g is the acceleration due to gravity.
• The friction force opposing the motion is given by the coefficient of kinetic friction (μ) times the normal force, where the normal force is m1 * g.

2. Set up equations of motion for the two blocks:

• For the block on the table: m1 * a = T - μ * m1 * g
• For the hanging block: m2 * g - T = m2 * a

3. Solve the two equations simultaneously to find the values of 'a' and 'T'.

In this case, the acceleration of the system is 1.68 m/s² and the tension in the string is 11.52 N.