Block A with mass 4 kg is at rest on a rough horizontal table, is connected to block B with mass 8 kg by a light inextensible string passing over a frictionaless pulley.

Question

A force F1 of magnitude 96 N is applied vertically upwards on block B .
Aforce F2 of magnitute 75N is now applied at an angle of 25 degrees with the horizontal on block A and the block accelerates to the left. The kinetic frional foce on block A is 11,76 N ignore the effects of air friction.
1. calculate the magnitude of the Tension in rope connected to block A ?

Answer 1

To calculate the tension in the rope connected to block A, we first need to find the acceleration of the system.

First, let's find the net force acting on block A:
Net force on block A = Tension in rope - Kinetic frictional force
Net force on block A = T - 11.76 N

Next, let's find the acceleration of the system using Newton's second law:
Net force on block A = mass of block A * acceleration
T - 11.76 N = 4 kg * acceleration
T = 4 * acceleration + 11.76 N

Now, let's find the net force acting on block B:
Net force on block B = Applied force - Tension in rope
Net force on block B = 96 N - T

Since both blocks are connected by a light inextensible string passing over a frictionless pulley, the acceleration of block A will be the same as block B.

Therefore, we can set up an equation to find the acceleration:
96 N - T = 8 kg * acceleration
96 N - 4 * acceleration - 11.76 N = 8 * acceleration
84.24 N = 12 * acceleration
Acceleration = 7.02 m/s^2

Now that we have found the acceleration, we can plug it back into the equation for T to find the tension in the rope connected to block A:
T = 4 * 7.02 + 11.76 N
T = 28.08 + 11.76
T = 39.84 N

Therefore, the magnitude of the tension in the rope connected to block A is 39.84 N.