Question

Two blocks are connected by a rope that passes over a set of pulleys. one block has a weight of 412 n,, and the other block has the weight of 908n. the rope and pulleys are massless and frictionless. a) find the acceleration of the lighter block

Answer 1

To find the acceleration of the lighter block in a system of two connected blocks, we need to consider the forces acting on the blocks. By setting up equations for the tension in the rope and the net forces on each block, we can solve for the acceleration. In this case, the acceleration of the lighter block is approximately 2.29 m/s^2.

Step-by-step explanation:

To find the acceleration of the lighter block, we need to consider the forces acting on the system. Since the rope and pulleys are massless and frictionless, the tension in the rope is the same throughout the system. Let's denote the acceleration of the system as 'a'.

For the lighter block, the net force acting on it is the tension in the rope minus its weight (412N). So we have:

Tension - 412 = mass x acceleration

Similarly, for the heavier block, the net force acting on it is the weight of the heavier block (908N) minus the tension in the rope:

908 - Tension = mass x acceleration

Since the tension in the rope is the same for both blocks, we can set these two equations equal to each other:

Tension - 412 = 908 - Tension

Solving for Tension gives us 660N. Plugging this value back into either of the original equations, we can solve for the acceleration. In this case, the acceleration of the lighter block is approximately 2.29 m/s^2.