Question

a block with a mass of 3 kg is swung on a cord in a horizontal circle with a radius of 2m. the speed of the block is 6m/s^. the magnitude of the acceleration of the block is most nearly

Answer 1

Given Information:  

Mass = m = 3 kg

Speed = v = 6 m/s  

Radius = r = 2 m

Required Information:  

Magnitude of the acceleration = a = ?  

Answer:

Magnitude of the acceleration = 18 m/s²

Explanation:

The acceleration of the block traveling along a circular path with some velocity is given by

a = v²/r

a = 6²/2

a = 36/2

a = 18 m/s²

Therefore, the magnitude of the acceleration of the block is most nearly equal to 18 m/s².

Bonus:

The corresponding force acting on the block can be found using

F = ma (a = v²/r)

F = mv²/r

Answer 2

Answer:

Acceleration = 18m/s².

Explanation:

Given m= 3kg, r = 2m, v = 6m/s

acceleration = v²/r = 6²/2 = 18m/s²

This acceleration is always directed towards the center of the center of the circular path of motion. Although the velocity v is constant the a body moving in a circular path is still accelerating because the direction of its velocity changes with time. Since velocity and acceleration are vectors, any change in the magnitude or direction in the velocity will cause affect the change in the magnitude and direction of the acceleration. The acceleration is always perpendicular to the direction of velocity.