Work Done, Energy Transfer, and Final Speed Calculation

What are the calculations needed to determine the work done, energy transferred, and final speed of the roller skate?

In this scenario, a force of 10.0 N acts on a 2.00 kg roller skate initially at rest on a frictionless table. The skate travels 3.00 m while the force acts. How much work is done, how much energy is transferred to the skate, and what is the final speed of the skate?

Answers:

The work done is 30.0 J, the energy transferred is also 30.0 J, and the final speed of the skate can be found by using the given work value in the equation (1/2)mv^2.

To calculate the work done on the roller skate, we can use the formula: Work = Force x Distance. In this case, the force is 10.0 N and the distance is 3.00 m. Therefore, the work done is: Work = 10.0 N x 3.00 m = 30.0 J. Since work is the transfer of energy, the amount of work done is equal to the energy transferred, which is 30.0 J. To find the final speed of the skate, we can use the equation for kinetic energy: Kinetic energy = (1/2)mv^2. Substituting the values, we can solve for v to find the final speed of approximately 3.87 m/s.