1. A roller coaster with a mass of 800 kg sits stationary at the top of a section of track, 75 m above

the ground as shown. When the brake is released, it starts to roll down the track


2. For each height represented in the diagram, calculate the gravitational potential energy using

Ep = mgh. Show ONE SAMPLE calculation in the calculations section below and fill in Table 1 for

each of the heights of the roller coaster. (6 marks)


3. Assuming there is no friction, determine the mechanical kinetic energy using Ek = Etotal - Ep.

Show ONE SAMPLE calculation in the calculations section below and fill in Table 1 for each of

the heights of the roller coaster. (6 marks)


4. For each height represented in the diagram, calculate the velocity using = �2

. Show ONE

SAMPLE calculation in the calculations section below and fill in Table 1 for each of the heights of

the roller coaster. (6 marks)


5. Use your answers to graph how gravitational potential energy, mechanical kinetic energy, and

velocity change as the roller coaster changes height. Use different colours for the three lines on

the graph. Graph paper is provided below. (3 marks)


6. Repeat steps 1 – 5 above for a roller coaster cart that has a mass of 300 kg and enter your

results in Table 2.

Calculations:

800 kg roller coaster cart:

Sample calculation for gravitational potential energy:

Sample calculation for Mechanical kinetic energy:

Sample calculation for velocity:


300 kg roller coaster cart:

Sample calculation for gravitational potential energy:

Sample calculation for mechanical kinetic energy:

Sample calculation for velocity:


Results:

Table 1: Potential energy, kinetic energy, total energy, and velocity of the 800 kg roller coaster cart


Table 2: Potential energy, kinetic energy, total energy, velocity of the 300 kg roller coaster cart.


Graphs:

It’s graphing time. These graphs are a bit different than the ones you did in the

data analysis assignment at the beginning of the course. In this case you have

three things to graph on each graph. (One graph for the 800 kg roller coaster cart

and one graph for the 300 kg roller coaster cart.) You need to graph the

gravitational potential energy with respect to height, the mechanical kinetic

energy vs height, and the velocity vs height.

Let’s look at the energy graphs first. In this case both kinetic energy and

mechanical energy cover the same range of values. This means they can use the

same scale on the y-axis. So, you will use the left y-axis and the x-axis to graph

the kinetic energy vs height and the potential energy vs height. You will need a

legend to explain which line is which. Colour coding is a nice way to highlight this.

The velocity values are much different than the energy values. This means you

need a totally different scale. So, your left y-axis won’t work. You need to make a

second scale on the right y-axis for your velocity values. You will plot the points

the same way as normal, but you will use the numbers on the right-hand scale

instead. Again, be sure to add your velocity line to the legend with a separate

colour code.


Discussion Questions:

1. Describe the relationship between the gravitational potential energy and the mechanical kinetic

energy of the roller coaster on your graph. (2 marks)

2. Describe the shapes of each of the three lines in the graph. Explain why the velocity is different.

(4 marks)

3. Describe how mass affects the speed at the bottom of the roller coaster. (2 marks)

4. Describe how mass affects the gravitational potential energy and the mechanical kinetic energy

of the roller coaster. (2 marks)

5. At what point does the roller coaster have a maximum value for the following? Justify your

answer by explaining why. (2 marks each)

a. Gravitational potential energy

b. Mechanical energy

c. Velocity

6. In your calculations, you assumed that the roller coaster was frictionless. All real roller coasters

encounter friction. Describe how the actual values of the variables would differ, or not differ,

from your calculated values for a real roller coaster. (Hint: what form of energy would some of

the total energy be converted to if there was friction in the system?) (4 marks)

How you will be graded:

Grades will be based on answering questions to demonstrate an understanding of the material covered

in this unit. Point form answers are okay if ideas are complete and use vocabulary (Word Bank)

provided. For questions out of 4 marks, there are 4 responses expected.

Answer:

Give me some hint please

Based on the calculations, potential energy of this roller coaster at a height of 75 meters is equal to 588,000 Joules.

Mathematically, potential energy is calculated by using this formula:

P.E = mgh

Where:

Note: Acceleration due to gravity is equal to 9.8 m/s².

At a height of 75 m, we have:

P.E = 800 × 9.8 × 75

P.E = 588,000 Joules.

At a height of 60 m, we have:

P.E = 800 × 9.8 × 60

P.E = 470,400 Joules.

At a height of 45 m, we have:

P.E = 800 × 9.8 × 45

P.E = 352,800 Joules.

At a height of 30 m, we have:

P.E = 800 × 9.8 × 30

P.E = 235,200 Joules.

At a height of 15 m, we have:

P.E = 800 × 9.8 × 15

P.E = 117,600 Joules.

In conclusion, we can deduce that the potential energy of this roller coaster decreases with a decrease in height.

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