Question

Two blocks are connected by a rope that passes over a massless and frictionless pulley as shown in the figure below. Given that m1 = 15.97 kg and m2 = 10.48 kg, determine the magnitudes of the tension in the rope and the blocks' acceleration. T = N a = m/s2 (Enter the magnitude.)

Answer 1

The tension in the rope is equal to the weight of the heavier block, which is 15.97 kg * 9.81 m/s^2 = 157.1 N. The acceleration of the blocks is equal to the net force acting on them divided by their total mass, which is (159.7 N - 104.8 N) / (15.97 kg + 10.48 kg) = 1.62 m/s^2.

Step-by-step explanation:

Consider the forces acting on each block:

Block 1: Gravity (15.97 kg * 9.81 m/s^2) and tension in the rope (T)

Block 2: Gravity (10.48 kg * 9.81 m/s^2) and tension in the rope (T)

Since the pulley is massless and frictionless, the tension in the rope is the same for both blocks.

Let's call this tension T.

Step 1: Set up the equations of motion

For block 1:

T - 15.97 kg * 9.81 m/s^2 = 15.97 kg * a

For block 2:

10.48 kg * 9.81 m/s^2 - T = 10.48 kg * a

Step 2: Solve for T and a

Adding the two equations above, we get:

0 = 5.49 kg * a

Therefore, a = 0 m/s^2.

Substituting this value of a back into either of the original equations, we can solve for T:

T = 15.97 kg * 9.81 m/s^2 = 157.1 N

Answer:

The tension in the rope is 157.1 N and the acceleration of the blocks is 0 m/s^2.