Block which is on a table has a mass of and block which is hanging from the pulley over the edge of the table has a mass of . If the acceleration of the blocks is , calculate the tension in the cable and the coefficient of friction between the block and the table.

Answer 1

To solve this problem, we need to apply Newton's second law of motion to both blocks.

For block on the table (Block 1):
Net force = Tension in the cable - frictional force
Mass * acceleration = T - μ * Mass * g
0.8 * 2 = T - μ * 2 * 9.8
1.6 = T - 19.6μ (equation 1)

For block hanging from the pulley (Block 2):
Net force = Tension in the cable - Weight of the block
Mass * acceleration = T - Mass * g
1 * 2 = T - 2*9.8
2 = T - 19.6 (equation 2)

Now, we need to solve these two equations simultaneously to find the tension (T) and the coefficient of friction (μ).

From equation 2, T = 2 + 19.6 = 21.6 N

Now, substitute T = 21.6 into equation 1:
1.6 = 21.6 - 19.6μ
19.6μ = 20
μ = 20/19.6
μ ≈ 1.02

Therefore, the tension in the cable is 21.6 N and the coefficient of friction between the block and the table is approximately 1.02.