Skate Park PBLTeam Members:

Xia Nan (23)Tan Jun Yang (19)

Xu Guiyi (24)

This is the skate park designed by our group. It seems to be very simple compared to the patterns designed by other groups, but it’s a more feasible one. Besides, our group concentrates on the calculations behind it :D

We want to put the skate park on the playground of Hwa Chong institution. Due to the limited space, we design that the height of the circle at the middle of the skate park is 12 meters, which is not so high. Besides, we make an arbitrary rule that, the average weight of a Hwa Chong student is 50 kg.

12 m

What should be the height of the starting point of the skate park?

While, the only data we have is the height of the circle in the middle part which is 12 meters.

Here, we have to talk about the friction:

As the type of friction between the skater and the track is rolling friction.

According to the formula of rolling friction: f=μ′W, here W represents the weight of the skater, and μ′ represents the coefficient of friction.

However, μ′ on the normal road is about 0.010, and the value can be even smaller if we choose appropriate materials. Therefore, the rolling friction before point A is negligible.

A

We all know that the kinetic energy can be calculated by using the formula:

And the gravitational potential energy can be calculated by using the formula:

As the initial velocity of the skater is 0,which means there is no kinetic energy. Therefore, the total energy at the beginning is , h represents the height of the starting point.

However the situation at the top of the circle is different, and we have to consider both the kinetic energy and the potential energy.

Here R represents the radius of the circle.

Here, we know the value of the mass of a student, we know the value of R, and g is a constant.

The only variable we don’t know here is the velocity at the highest point of the circle. How to solve the problem?

Here, we have to introduce the knowledge of the circular motion. As the friction are ignored before the point A on the track, we can use the formula of the circular motion here.

The only force exerts on the skater at the highest point of the circle is gravitational force. While the acceleration of the skater is . According to the second Newton’s law, , the force that exerts on the skater can also be represented as .

Then we come back to the original equation:

We also have another equation:

Therefore the value of h is derived, which is equal to 2.5 R.

h𝑚𝑔 =12𝑚𝑣2+𝑚𝑔×2𝑅

From the calculation above, we have derived that the initial position of the skater is 15 meters above the ground.

How to stop the skater at the end of the skate park? We have to consider the case comprehensively.

The ending point cannot be so high, or it will be difficult for the skater to get down. Therefore, we have to change the material of the track in order to increase the friction between the skater and the track.

What we design is that:

We let the track go up by one meter, then we keep the track flat, which means the height of the skater’s position is keep constant after he reaches the point A.

So, how much energy is left after he passes the point A?

So, the energy left must be used the compensate the friction.

Here, we select another kind of material with the μ′ being 0.10, which is the same as the muddy ground.

According to the formula to calculate the work done:

In order to obtain the value of S (distance), we have to know the value of friction.

According to the formula of friction mentioned before:

Therefore

15meters

12 meters

14 meters

1 meter

The labeled diagram

= 0.10

This is our design, Do you like it?

Dear Ms. Tan,

Here, I represent my group to apologize faithfully for our late submitted work, and the inconvenience caused by us. We have done a reflection on our teamwork, and we have realized the great importance of collaboration and being responsible. We promise that the similar issue won’t occur again!

Thank you and sorry Ms. Tan,Xia Nan

Dear Ms. Tan,

After this incident, I have realized the importance of effective communication and teamwork. I am sorry that due to our miscommunication that this piece of work has to be submitted so late and that I will be responsible in doing teamwork. I apologize for the trouble caused and I will not repeat this again.

Thank you and sorry Ms. Tan,Jun Yang

Dear Ms. Tan,

This incident has taught me that the importance of teamwork cannot be overlooked. I should have been be more aware of the PBL work and that this PBL has taught me to talk to my friends to understand the situation better

Thank you and sorry Ms. Tan,Gui Yi