Question

If a block is subjected to a force of 500 N, determine its velocity when s = 0.5 m. When s = 0, the block is at rest and the spring is uncompressed.

Answer 1

The velocity of the block when the displacement is 0.5 m is 31.6 m/s.

Step-by-step explanation:

To determine the velocity of the block when the displacement (s) is 0.5 m, we need to use the principles of work and energy. The work done on an object is equal to the force applied on the object multiplied by the displacement in the direction of the force. In this case, the work done on the block is equal to the force applied (500 N) multiplied by the displacement (0.5 m).

Using the equation:

Work = Force x Displacement

W = F x s = (500 N) x (0.5 m) = 250 J

The work done on the block is equal to the change in its kinetic energy. Therefore, we can set up the equation:

Work = Change in Kinetic Energy = (1/2) m v^2

Where m is the mass of the block and v is its velocity.

250 J = (1/2) 0.5 kg v^2

Simplifying the equation, we find:

v^2 = 1000

v = √1000 = 31.6 m/s

Therefore, the velocity of the block when the displacement is 0.5 m is 31.6 m/s.