Question

One common application of conservation of energy in mechanics is to determine the speed of an object. Although the simulation doesn’t give the skater's speed, you can calculate it because the skater's kinetic energy is known at any location on the track. Consider again the case where the skater starts 7 m above the ground and skates down the track. What is the skater's speed when the skater is at the bottom of the track? Express your answer numerically in meters per second to two significant figures.

Answer 1

The skater's speed at the bottom of the track can be determined using the law of conservation of energy.

Step-by-step explanation:

The skater's speed at the bottom of the track can be determined by applying the law of conservation of energy. At the top of the track, the skater has only potential energy, which is converted to kinetic energy as the skater moves down the track. The potential energy at the top of the track can be calculated using the equation:

mgh = (1/2)mv2

where m is the mass of the skater, h is the height, and v is the speed of the skater. At the bottom of the track, all the potential energy is converted to kinetic energy, so we can set the potential energy equal to the kinetic energy:

mgh = (1/2)mv2

Rearranging the equation gives:

v = √(2gh)

Plugging in the values for mass (which is not given in the question) and height, you can calculate the skater's speed at the bottom of the track.

Answer 2

11.71 m/s

Step-by-step explanation:

In the absence of non-conservative forces, the mechanical energy which is the sum of kinetic energy and potential energy remains conserved. skaters kinetic energy down the track would be equal to potential energy at the top.

P.E. = m g h

where, m is the mass, g is the gravitational acceleration and h is the height.

K.E. = 0.5 m v²

where, v is the speed.

P.E. = K.E.

⇒m g h = 0.5 m v²

⇒v²= 2 g h

Substitute the values:

v² = 2 (9.8 m/s²) ( 7 m) = 137.2

⇒v = 11.71 m/s