Question
16. Block A which is on a table has a mass of 4 kg and block B which is hanging from the
pulley over the edge of the table has a mass of 16 kg. If the acceleration of the blocks is
3.2 m/s, calculate the tension in the cable and the coefficient of friction between the
block and the table.
pulley over the edge of the table has a mass of 16 kg. If the acceleration of the blocks is
3.2 m/s, calculate the tension in the cable and the coefficient of friction between the
block and the table.
Answers
GPT 3.5
To calculate the tension in the cable, we can consider the forces acting on block B. The tension in the cable pulling up on block B is equal to the force of gravity acting on block B, since the blocks are accelerating upwards.
Tension = Force of gravity on block B
T = m * g
T = 16 kg * 9.8 m/s^2
T = 156.8 N
Now, to calculate the coefficient of friction between block A and the table, we need to consider the forces acting on block A. The only horizontal force acting on block A is the friction force.
Friction force = Coefficient of friction * Normal force
Friction force = μ * m * g
Since block A is not accelerating vertically, the normal force acting on block A is equal to its weight.
Normal force = m * g
Normal force = 4 kg * 9.8 m/s^2
Normal force = 39.2 N
Friction force = μ * 39.2 N
The net force acting on block A in the horizontal direction is equal to the tension in the cable pulling block A, minus the friction force.
Net Force = T - Friction force
m * a = T - μ * m * g
Using the previously calculated values:
4 kg * 3.2 m/s^2 = 156.8 N - μ * 4 kg * 9.8 m/s^2
12.8 N = 156.8 N - 39.2 μ
39.2 μ = 144 N
μ = 3.67
Therefore, the tension in the cable is 156.8 N and the coefficient of friction between block A and the table is 3.67.
Tension = Force of gravity on block B
T = m * g
T = 16 kg * 9.8 m/s^2
T = 156.8 N
Now, to calculate the coefficient of friction between block A and the table, we need to consider the forces acting on block A. The only horizontal force acting on block A is the friction force.
Friction force = Coefficient of friction * Normal force
Friction force = μ * m * g
Since block A is not accelerating vertically, the normal force acting on block A is equal to its weight.
Normal force = m * g
Normal force = 4 kg * 9.8 m/s^2
Normal force = 39.2 N
Friction force = μ * 39.2 N
The net force acting on block A in the horizontal direction is equal to the tension in the cable pulling block A, minus the friction force.
Net Force = T - Friction force
m * a = T - μ * m * g
Using the previously calculated values:
4 kg * 3.2 m/s^2 = 156.8 N - μ * 4 kg * 9.8 m/s^2
12.8 N = 156.8 N - 39.2 μ
39.2 μ = 144 N
μ = 3.67
Therefore, the tension in the cable is 156.8 N and the coefficient of friction between block A and the table is 3.67.