Physics in Real life: Merry-Go-Around
Case Description:
A 40kg child is standing on the edge of a merry-go-around, which has a mass of 200kg. It is not moving initially. Then the child is walking on the edge of the merry-go-around and the merry-go-around starts to rotate in the opposite direction. It makes one revolution every 5 s. The moment of inertia of the merry-go-round (about an axis through its center) is 500 kg·m². We are trying to find the final angular velocity of the merry-go-around , the relative final angular velocity of the child to the ground, the force diagram of the child, the final rotational kinetic energy of the merry-go-around.
Image Illustration:
Case Description:
A 40kg child is standing on the edge of a merry-go-around, which has a mass of 200kg. It is not moving initially. Then the child is walking on the edge of the merry-go-around and the merry-go-around starts to rotate in the opposite direction. It makes one revolution every 5 s. The moment of inertia of the merry-go-round (about an axis through its center) is 500 kg·m². We are trying to find the final angular velocity of the merry-go-around , the relative final angular velocity of the child to the ground, the force diagram of the child, the final rotational kinetic energy of the merry-go-around.
Image Illustration:
Now, how does this relate to some physics concepts specifically?
- Motion (velocity, acceleration, etc)
- When the merry-go around starts moving, there is angular velocity presented.
- When the child starts to walk on the edge of the merry-go-around, there is linear velocity presented.
- Forces
- When the child is standing on the stationary merry-go-around, there are both gravitational force and normal force acting on him.
- When the child is on the moving merry-go-around, there is a circular force acting on him.
- Energy
- When the merry-go-around is rotating, there will be the rotational kinetic energy.
- We will try to find the final rotational kinetic energy in the problem.
- Momentum
- Since there is no torque exerted on the child-merry-go-around system, the angular momentum is conserved.
- We can use the law of the conservation of momentum to help us to solve for this problem.
- Rotation
- The merry-go-around is rotating.
- We will use rotational kinetic energy, angular momentum, and angular velocity to solve for this problem.
Conclusion:
My problem discussed the physics concepts and discussed all of the areas: Motion (velocity, acceleration, etc), Forces, Energy, Momentum, and Rotation. I drew a force diagram and find the find the final angular velocity of the merry-go-around , the relative final angular velocity of the child to the ground, the force diagram of the child, the final rotational kinetic energy of the merry-go-around.
My problem discussed the physics concepts and discussed all of the areas: Motion (velocity, acceleration, etc), Forces, Energy, Momentum, and Rotation. I drew a force diagram and find the find the final angular velocity of the merry-go-around , the relative final angular velocity of the child to the ground, the force diagram of the child, the final rotational kinetic energy of the merry-go-around.
Accident Reconstruction Activity Report
Case Description:
On January 17, 2018, an automobile accident occurred at the intersection of Furiosa Dr. and Fury Rd. in Joule, VA between a compact car (driven by Mike Rokar) and a tractor-trailer (driven by Lincoln Hawk). Mr. Rokar claims that he “has made a full stop at the light before entering the intersection” while Mr. Hawk claims that he “has been braking before the collision”. For more details about the collision, please look at the Crash Details section here.
Video
Case Description:
On January 17, 2018, an automobile accident occurred at the intersection of Furiosa Dr. and Fury Rd. in Joule, VA between a compact car (driven by Mike Rokar) and a tractor-trailer (driven by Lincoln Hawk). Mr. Rokar claims that he “has made a full stop at the light before entering the intersection” while Mr. Hawk claims that he “has been braking before the collision”. For more details about the collision, please look at the Crash Details section here.
Video
Image
Background Information:
In order to determine which driver is at fault in this case, it is necessary to review some of the basic physics concepts on forces & motion, work & energy, friction, conservation of momentum, and kinematics:
In order to determine which driver is at fault in this case, it is necessary to review some of the basic physics concepts on forces & motion, work & energy, friction, conservation of momentum, and kinematics:
- Since there is no information on the initial velocity and final velocity of both the car and the truck, it will be helpful to start the calculations that determine the coefficient of kinetic friction between the tires and the road for both the car and the truck. The coefficient of kinetic friction only applies to an object that is moving (hence “kinetic”) and is otherwise known as sliding friction. Friction is the force that opposes the sliding motion (braking in this case).
- Using friction, net forces, and work equations to determine the speed of both vehicles right after the collision. Work is the measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement. According to the principle of work and kinetic energy (also known as the work-energy theorem), the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle
- Using the law of the conservation of the momentum to determine the speed of both vehicles right before the collision. The conservation of momentum law means that the total linear momentum of a system of particles not acted upon by external forces is constant in magnitude and direction irrespective of any reactions among the parts of the system (total momentum before = total momentum after, p before = p after, (m1v1 + m1v1)i = (m1v1 + m1v2)f).
- Use all the values we got to test whether the drivers are speaking the truth or not.
Calculations
Step 1 - Finding the Coefficient of Kinetic Friction
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Step 2 - Finding the Speed After the Collision
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Step 3 - Finding the Speed Before the Collision
- The conservation of momentum law means that the total linear momentum of a system of particles not acted upon by external forces is constant in magnitude and direction irrespective of any reactions among the parts of the system, which the same case under this situation.
- Two dimension collision happened herel. Therefore, the momentum will be conserved in each direction independently if there is no external force in that direction. In other words, the total momentum in the x-direction will be the same before and after the collision.
- Initially, the car only moves in the y-direction and the truck only moves x-direction, which means that...
- (Mc)(Vi,xc) equal 0.
- (Mt)(Vi,yt) equal 0.
- In addition to the values we have, we also need to remember that θ for the truck is 7 degrees while θ for the car is 33 degrees. Also, we need to convert the mass of the car and the truck to the kilogram, which is the IS Unit.
- In the x-direction, we can write the equation.
(Mc)(Vi,xc)+(Mt)(Vi,xt)=(Mc)(Vfc)(cosθc)+(Mt)(Vft)(cosθt).
In this equation, “c” stands for the car, and “t” stands for the truck. In the y-direction, we can write the equation:
(Mc)(Vi,yc)+(Mt)(Vi,yt)=(Mc)(Vfc)(sinθc)+(Mt)(Vft)(sinθt).
The speed of the car before the collision is 12.781 m/s.
The speed of the truck before the collision is 12.509 m/s.
- Vi,xc = the initial velocity of the car in the x-direction
- Vi,yt = the initial velocity of the truck in the y-direction
- Vcf = the speed of the car after the collision
- Vtf = the speed of the truck after the collision
Conclusion
Presentation Slide
- Both drivers are at fault because they all lie in their claims:
- Mr. Rokar did not made a full stop at the light before entering the intersection;
- Mr. Hawk did not brake before the collision. He did not drive in 6.7m/s
Presentation Slide
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Bowling Ball and Broom Stick Activity
The graph below shows the path of the bowling ball and the direction of the force applied on the bowling ball. Force is the ability to cause a change in state of motion of an object. Force is a vector, which means that it has both magnitude and direction. What I should improve is that the length of the arrows should varied because we applied forces when the ball was at different point on the path. For example, the force on the ball would be smaller when we were pushing the ball straight forward. However, when we were trying to make a turn of the bowling ball, the force we were applying should be bigger. Inertia plays a part in it. Inertia is a tendency of an object to resist a change of state of motion. When we were trying to change the direction the ball is traveling, we needed to apply a force toward the center. Since the mass of the bowling is large, it is hard to more because more mass means more inertia, matter and weight. Mass is a measure of inertia, which is the measure of an objects resistance to acceleration. In the no-touch zone, the ball is going to roll forever if there is no resistance because of inertia.
The graph below shows the path of the bowling ball and the direction of the force applied on the bowling ball. Force is the ability to cause a change in state of motion of an object. Force is a vector, which means that it has both magnitude and direction. What I should improve is that the length of the arrows should varied because we applied forces when the ball was at different point on the path. For example, the force on the ball would be smaller when we were pushing the ball straight forward. However, when we were trying to make a turn of the bowling ball, the force we were applying should be bigger. Inertia plays a part in it. Inertia is a tendency of an object to resist a change of state of motion. When we were trying to change the direction the ball is traveling, we needed to apply a force toward the center. Since the mass of the bowling is large, it is hard to more because more mass means more inertia, matter and weight. Mass is a measure of inertia, which is the measure of an objects resistance to acceleration. In the no-touch zone, the ball is going to roll forever if there is no resistance because of inertia.
- Change in motion --> Acceleration --> a=change in velocity / change in time
Space Station Blog Post (Green Park Space Station)
- Purpose: Our vision for the space station is that scientists will be able to develop high technology and do specific experiments here. It is necessary because some research and technologies need to be conducted in space where there is no gravity or damage to the environment, such as no-gravity environment for Parkinson’s research, cancer research in space and recycling in space. This space station will serve scientists and researchers as well as companies to live and conduct experiments in space. Also, this space station provide a living environment for people who wants to try to stay in the space for a while.
- Constraints: (Lists costs and cost calculations are shown below)
- Constraints: Under budget ($8517310466<$1600000000)
Annual Income:
Cost of Rooms: $26,510,000Cost of materials, tangential speed, altitude, and orbital speed: $8,490,800,466 (work on next page)
Total Cost: $8,517,310,466
Residential Income: $400,000Luxury Suites Income: $5,000,000
Advertising Income: $1,000,000
Science Lab Income: $10,800,000
Diplomat Income ($10,000,000 per Country/Corporation that wishes to use it)
Total Income: : $ 17,200,000+$10,000,000 per country
If 50 countries/corporations agree to join according to our relatively low price, then we will make our return within 20 years.
- Potential: It is important because companies can take advantage of the space station to develop more advanced products without causing damage to the environment on Earth. Companies and nations will benefit because they can use the station to research in a zero-g space environment and conduct research that is not ordinarily possible. Also, citizens can take the chance to travel to space to live for a while. Hence, companies can earn more money from doing commercial on the space station. Our space station is better than other space stations with a similar purpose because this space station is not only about science, but also residents can have a decent life at here since there are a lot of fun activities available for them.
- Universal Law of Gravitation: This law states that two objects attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.The altitude of the space station will be 200000 m, which is lower than the International Space Station. The key reason for moving to this altitude is to save propellant over the long term as we protect against increased solar activity of the space station. According to Systems Engineering, Analysis and Integration Office: "as solar activity rises, the atmospheric density in our altitude range increases causing increased drag on the vehicle. This in turn causes us to have to raise the orbit more often." The tangential speed for our space station will be 56m/s. Both calculation and the force diagram will be shown below.
- Centripetal Acceleration:
- Material Area: S=2πrh=2*π *400m (radius of the space station)*50m (height of the space station)=125663.706144 m²
- Material Mass: 125663.706144m² * 20kg/m² =2513274 kg
- Speed of Rotation is shown below
- Orbit is shown below
- Two dimensions