Question

b. Compare what happens to potential energy, kinetic energy, and total energy as the skater moves up and down the track. What general statement can you make about the relationship between potential and kinetic energy?

c. Notice that the bar entitled “Thermal” energy does not deviate from zero. This represents an energy that is transformed into "heat" energy. What must be true of this skate park for this to remain at zero?

d. Vary the skater's Mass with the slider on the right while the simulation is running. Describe the similarities and differences that changing the mass has on the bar graphs.

e. Click on the Friction tab at the bottom and choose the parabola track. Place the skater at the top. Examine the bar graphs as the skater oscillates back and forth. What is happening to the energies present? Explain how you know that energy is still being conserved.

f. Run the simulation as in part “e” until the skater comes to a stop. What form did the skater’s initial energy end up as?

Use the above graphs to answer the questions below. a. Estimate roughly where was he located at the times listed below:

• zero seconds? ___________________

• 6.8 seconds? __________________

• 8.1 seconds? _________________

• 5.3 seconds? _________________

b. If his maximum height is 4 m (measured from the bottom of the track), what is his height at the times below

• zero seconds? ___________________

• 6.8 seconds? __________________

• 8.1 seconds? _________________

• 5.3 seconds? __________________

Examine the kinetic energy curve on the graph above. Given that his mass was 75kg calculate his speed at the times below using Ek = ½mv2 .

Speed at zero seconds: show any work below v0 = ______________ m/s

Speed at 6.8 seconds: show any work below v0 = ______________ m/s

Speed at 8.1 seconds: show any work below v0 = ______________ m/s

Speed at 5.3 seconds: show any work below v0 = ______________ m/s

Choose the Friction tab (bottom of screen) and select the half-pipe track. Now select on Grid. This will provide a scale for you to measure heights in meters. You may assume that the mass of the default skater is 75kg. Run the simulation and sketch the Energy vs time graphs below. You know the shapes of these from above, you simply need to determine the transition times (period of motion). Use a stopwatch to get a rough idea. Be sure to include a legend to represent your different energy curves.

Answer 1

Solution of b:

When the friction is off: when skater goes up it they achieve maximum potential energy and zero kinetic energy while when skater goes down they achieve maximum kinetic energy and zero potential energy. Therefore, we can say that when the friction is off, there is energy conservation i.e. total energy of the skater remains same all the time but as skater moves up and down, the kinetic and potential energy conversion occurs. In this scenario, the skater infinitely moves up and down.

When the friction if on: when skater goes up it they achieve maximum potential energy and zero kinetic energy while when skater goes down they achieve maximum kinetic energy and zero potential energy. Since friction is on, the part of total energy converts into thermal energy slowly. Moreover, the friction force is non conservative, and for this reason, the friction force converts total energy gradually into thermal energy and eventually skater comes to down and stops movement. In this scenario, the skater doesn’t move up and down infinitely.

Solution of c:

As explained earlier, to "Thermal" bar remain zero, there must not be any friction between skater and the track surface when skater moves up and down.

Solution of d:

As the mass of the skater is increased, there is no any change in the skater's movement compare to when skater's mass is small. But as skater's mass increases, the total energy increases and as mass decreases the total energy decreases. Therefore, we can conclude that total energy is directly proportional to skater's mass. Since total energy is equal to sum of potential energy, and kinetic energy, each energy is directly proportional skater’s mass.

The potential energy of the skater is given as:

Where is the mass of the skater, is the gravitational acceleration and is the height of the skater.

The kinetic energy of the skater is given as:

Where is the speed of the skater.

Solution of e:

when skater goes up it they achieve maximum potential energy and zero kinetic energy while when skater goes down they achieve maximum kinetic energy and zero potential energy. Since friction is on, the part of total energy converts into thermal or heat energy slowly. Moreover, the friction force is non conservative, and for this reason, the friction force converts total energy gradually into thermal energy and eventually skater comes to down and stops movement. We know this because at any time the total energy is the sum of potential energy and kinetic energy and thermal energy.

Total energy is given as:

Where is the potential energy, is the kinetic energy, and is the thermal energy.

Solution of f:

When skater comes to stop, the all initial energy is converted into thermal energy because of the friction. Note that the friction force is non conservative, and for this reason, the friction force converts total energy gradually into thermal energy and eventually skater comes to stop.

Solution of a:

• At zero seconds the skater is located at the top of the track.
• At 6.8 seconds the skater is located at the 2 m from the ground.
• At 8.1 seconds the skater is located at the 1 m from the ground.
• At 5.3 seconds the skater is located at the 1.5 m from the ground.

Solution of b:

• At zero seconds the skater is located at the 4 m from the ground.
• At 6.8 seconds the skater is located at the 0.8 from the ground.
• At 8.1 seconds the skater is located at the 0.5 from the ground.
• At 5.3 seconds the skater is located at the 2.1 m from the ground.

Now mass of the skater , the skater's speed at different time can be calculated from energy conservation:

At zero seconds the skater is located at the 4 m from the ground.

At 6.8 seconds the skater is located at the 0.8 from the ground.

At 8.1 seconds the skater is located at the 0.5 from the ground.

At 5.3 seconds the skater is located at the 2.1 m from the ground.