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?

Answer 1

To determine the skater's speed at the bottom of the track, we can equate the initial potential energy to the final kinetic energy and solve for v.

Step-by-step explanation:

When the skater is at the bottom of the track, all of their initial potential energy has been converted to kinetic energy. The conservation of energy principle states that the total energy of an isolated system remains constant. In this case, the skater starts with gravitational potential energy at the top of the track, and as they skate down, this potential energy is transformed into kinetic energy. So, to determine the skater's speed at the bottom of the track, we can equate the initial potential energy to the final kinetic energy:

mgh = (1/2)mv^2

In this equation, m represents the mass of the skater, g is the acceleration due to gravity, h is the height of the skater above the ground at the start, and v is the velocity or speed of the skater at the bottom of the track. By rearranging the equation and solving for v, we can calculate the skater's speed.

Answer 2

Answer:v=11.71 m/s

Step-by-step explanation:

Given

Skater is at a height of 7 m above the ground and skate down the track

Conserving Energy At top and Bottom point

Potential Energy converted to Kinetic Energy

Potential Energy
`=mgh`

Kinetic Energy
`=(mv^2)/(r)`

`mgh=(mv^2)/(2)`

`v=√(2gh)`

`v=√(2* 9.8* 7)`

`v=√(137.2)`

`v=11.71 m/s`