Effect of Object Speed on Velocity, Acceleration, Force and Energy

Background Research:

Formulae:

• Velocity- $\frac{\mathrm{Distance}}{\mathrm{Time}}$
• Acceleration- $\frac{{\mathrm{V}}_f–{\mathrm{V}}_i}{\mathrm{Time}}$
• Force- $\mathit{mass}\times \mathit{acceleration}$
• Kinetic Energy- $\frac{1}{2}\mathit{mass}\times {\mathit{final\; velocity}}^2$

Sphero’s components

Spheros are basic robots made for education and fun. The Sphero 2.0 is a tiny robot, inside a white translucent casing, that uses a gyroscope to balance on two wheels. It may not seem that the Sphero has a front or back, but inside the robot there is, due to the gyroscope. When a Sphero is commanded to drive in a new direction, it’s able to rotate to face the right way based on its position relative to the user. To control the Sphero, it must be connected to a device via Bluetooth pairing. When the user starts the Sphero Drive app and uses the joystick to control the robot, the touch to control the robot is converted into a given speed which is communicated to the robot via Bluetooth. The Sphero drives like a hamster wheel spins, the robot drives up the side of its own shell, then gravity pulls it down and the shell falls beneath it. This causes the Sphero to roll. In a way, the Sphero runs on gravity.

Collisions

A collision is a situation in which two objects bump into one another and energy changes in form or move from one thing to the other. When two things hit each other, or collide with each other, they exchange energy. Energy can’t be created or destroyed, however, it can be converted from one form to another, and it can also be shifted form one object to another. When a ball hits the ground, kinetic energy is transformed into sound and heat energy, which causes the ball to change its shape. An example of a collision is a car crash without seatbelts. Seat belts are designed to restrain the wearer so that they move with the car, and stop with the car, during the impact. When a passenger of a car doesn’t wear a seatbelt during a car crash, the passenger keeps moving even though the car stops suddenly, which is what Isaac Newton’s first law of motion states, “An object in motion tends to stay in motion and an object at rest tends to stay at rest unless acted upon by an unbalanced force.” In this scenario, the object is the passenger, so if the car stopped, the person would keep moving at the same speed without a seatbelt until they come in contact with a solid object such as the windscreen or steering wheel.

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There are two types of collisions, elastic and inelastic collisions. An elastic collision is where there is no loss in kinetic energy in the system as a result of the initial collision. Both momentum and kinetic energy are both protected quantities in elastic collisions. For example, two trolleys are speeding towards each other with equal speed. They collide and bounce off each other with no loss in speed. This collision is perfectly elastic because no energy has been lost. These collisions usually partake between atoms and gases.

An inelastic collision is where there is a loss in kinetic energy. While momentum of the system is protected in an inelastic collision, kinetic energy is not. This is because some kinetic energy had been moved to something else. Thermal energy, sound energy, and material are sometimes the cause. With the same example as the last, there are two trolleys speeding towards each other. They collide, but because the trolleys have magnets on them, they join together during the collision and become one connected mass. This collision is perfectly inelastic because the maximum amount of kinetic energy has been lost.

Practical Task

Aim: To investigate how the speed of an object affect its velocity, acceleration, force, and kinetic energy.

Materials: Sphero, trundle wheel or meter ruler, stopwatch/timer, iPad, Sphero cover,  

Procedure:

1. Using the trundle wheel, measure and mark off 10 meters on a carpeted floor.
2. Open the Lightning Lab APP and set Sphero to 25% speed (63.75 in Speed settings).

1. Drive the Sphero with no cover recording the time at 10 meters.
2. Repeat the test 2 more times and calculate the average time.
3. Next, set Sphero to 50% speed (127.50 in Speed settings).
4. Repeat it two more times and calculate the average time.
5. Next, set Sphero to 75% speed (191.25 in Speed settings).
6. Repeat it two more times and calculate the average time.
7. Next, set Sphero to 100% speed (255 in Speed settings).
8. Repeat it two more times and calculate the average time.
9. Using the data collected from the experiment, calculate Final Velocity, Acceleration, Force, and Kinetic Energy.
10. Answer question: How does the speed of an object affect its velocity, acceleration, force, and kinetic energy?

Results:

Discussion:

How does the Sphero´s set speed affect the time it takes for the Sphero to travel the 10 meters?

If the set speed of the Sphero is increased, then the time it takes the Sphero to travel the ten minutes will decrease. On the opposite hand, if the Sphero’s set speed is decreased, then the time it takes the Sphero to travel the ten metres will decrease. For example, if the Sphero’s speed was 25%, then it would take the Sphero longer to travel the ten metres than if it were set on 75% speed. The average velocity graph is non-linear, which means that the Sphero sped up quickly at first, but after reaching 50% and above, it sped up more slowly.

Using the average numbers only, explain how the set speed affects acceleration.

The lower the set speed of the Sphero, the lower the acceleration will be. To explain from the practical task, the average acceleration of the Sphero at 25% was 0.069702053 m/s², and the average acceleration for the Sphero at 100% was 0.621094461 m/s². This means that the acceleration increased when the speed increased. This happens because, in order for the Sphero to go fast, it needs to accelerate more to propel itself forwards and reach the ten metres. If the Sphero is set on 50% according to the results, it will only accelerate at 0.253469149 m/s² because the Sphero is set on a low speed and the Sphero doesn’t have the need to accelerate fast if it’s only going slow. If the speed was set at 75%, according to the results, it will accelerate at 0.462310225 m/s² because the Sphero needs to accelerate faster so it can go fast.

How does the force and kinetic energy change from one set speed to another? Why do you think this happens?

The force and kinetic energy increase as the set speed increases. According to the results, when the Sphero was set at 25% the average kinetic energy was 0.107 and the force was 12.7N and when the Sphero was set at 100% the kinetic energy was 1.131 and the force was 113.12N. Kinetic energy is the energy of an object’s movement, therefore, if the set speed of the Sphero is 25% then the kinetic will be low because it is moving slowly. On the other hand, if the set speed of the Sphero is 100% then the kinetic energy will be high because there is more movement to make the Sphero go fast. With the force, it is a linear equation, f=mass x acceleration. Meaning that if acceleration increases the force increases too so the graph is increasing because it has to go at a constant speed because the equation needs to be equal.

Extension: If we complete this same activity using a Cover on the Sphero, how might this affect the final velocity, acceleration, force and kinetic energy? What force would cause this change? Suggest another experiment that could also investigate this concept.

The nature of the flooring the Sphero is rolling on will change the variables and results of the experiment. If the ground was rough or bumpy it would affect the way the Sphero accelerates. Because the Sphero was driven on carpet, the speed at 25% made the Sphero speed up quickly however, the friction from the carpet caused the Sphero at speeds 50% and up to not reach the maximum potential acceleration.

Conclusion

The experiment was unsuccessful for the class; however, the aim was achieved. The experiment was unsuccessful because the class could not use the Spheros and record their own results. If they had the opportunities to record their own results or have working Spheros, the results would have been more varied throughout the class. Also, instead of evaluating speeds, it would have been more enjoyable and interesting if the experiment was focused on the Sphero being driven on different surfaces. So that the students would have been able to examine the changes in the Spheros behaviour on different surfaces.

Bibliography

• BBC Bitesize. (2019). Momentum and forcese. [online] Available at: https://www.bbc.com/bitesize/guides/z32h9qt/revision/3 [Accessed 2 Jun. 2019].
• Questacon – The National Science and Technology Centre. (2019). Collisions. [online] Available at: https://www.questacon.edu.au/discover/collisions [Accessed 2 Jun. 2019].
• Khan Academy. (2019). What are elastic and inelastic collisions?. [online] Available at: https://www.khanacademy.org/science/physics/linear-momentum/elastic-and-inelastic-collisions/a/what-are-elastic-and-inelastic-collisions [Accessed 2 Jun. 2019].
• Team, H. (2019). How the Sphero works – How It Works. [online] How It Works. Available at: https://www.howitworksdaily.com/how-the-sphero-works/ [Accessed 30 May 2019].