Question

A 422N block is sitting on a frictionless surface and is connected by a massless, extension-less rope over a frictionless pulley to a 185N mass. What is the acceleration of the blocks and the tension in the cable.

Answer 1

To find the acceleration of the blocks and the tension in the cable, we can use Newton's second law of motion and set up equations for the hanging mass and the block on the surface. Solving these equations will give us the values we need.

Step-by-step explanation:

Tension and Acceleration in a Two-Block System

In order to find the acceleration of the blocks and the tension in the cable, we can use Newton's second law of motion which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

In this system, the force of gravity acting on the hanging mass mg pulls it downward, while the tension in the cable T pulls it upward. Since the system is frictionless, the acceleration of both blocks will be the same and can be represented as a.

Applying Newton's second law to each block, we can set up the following equations:

For the hanging mass: mg - T = ma

For the block on the surface: T = mR

where m is the mass of the hanging block, g is the acceleration due to gravity, a is the acceleration of the system, and R is the mass of the block on the surface.

Solving these equations simultaneously will give us the value of the acceleration and the tension in the cable.

Answer 2

solution is written in attached image.