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Data
Measure the mass of your ball and the cup you are using.
Measure the height of your ramp and, therefore, the starting height of your ball.
Measure the distance traveled by the cup of three different trials, and find the average distance traveled.
Mass of Ball
(kg)Mass of the Cup
(kg)Initial Height of the Ball (m)Distance Traveled by the Cup (m)0.04550.01600.2200.2850.04550.01600.2200.2800.04550.01600.2200.3000.04550.01600.220Avg: 0.288
Calculations and Results
Calculate the potential energy of the ball before it is released and the kinetic energy right before it hits the cup. What assumption do you have to make to find the kinetic energy?
Potential Energy:
Ep = mgh
Ep = (0.0455 kg)*(9.81 m/s2)*(0.220m)
Ep = 0.0982 Joules
Kinetic Energy:
Energy before ball is released has to equal the energy right before the ball hits the cup according to the law of conservation of energy.
Right before the ball hits the cup, its height is 0 m; therefore, it only has kinetic energy.
Ep = Ek
Ek = 0.0982 Joules
To find the kinetic energy, you have to assume that there is no friction exerted on the ball as it rolls down the ramp. We also do not consider the rotational energy for this problem.
Calculate the velocity and momentum of the ball right before it hits the cup.
Velocity:
Ek = * m * v2 where m = mass of the ball and v = velocity of the ball
0.0982 Joules = * (0.0455 kg) * v2
v = 2.08 m/s
Momentum:
p = m * v where p = momentum, m = mass, and v = velocity
p = (0.0455 kg) * (2.08 m/s)
p = 0.0945 kg * m/s
Calculate the work done by friction to stop the ball.
W = Ef Ei where W = work, Ef = Final energy, and Ei = Initial Energy
W = 0 Joules 0.0982 Joules
W = 0.0982 Joules
Calculate the frictional force on the cup and the coefficient of friction between the cup and the surface. What assumption is being made?
Frictional Force:
The work done by the friction force was 0.0982 Joules
W = F * d where d = distance traveled, F = applied force (in this case, friction)
0.0982 Joules = F * 0.288 m
F = 0.341 Newton
Coefficient of Friction
Ff = * N where = coefficient of friction, N = normal force
0.341 Newtons = * (0.0455 kg + 0.0160 kg)(9.81 m/s2)
= 0.565
We are assuming that the coefficient of kinetic friction and the coefficient of static friction are equal. This makes the calculations much simpler.
Fill in the table below with your results.
Potential Energy (Joules)0.0982Kinetic Energy (Joules)0.0982Velocity (m/s)2.08Work (Joules)0.0945Momentum (kg*m/s)0.0982Frictional Force (Newton)0.341Coefficient of Friction0.565Further Learning
By what factor would the velocity of the ball right before it hits the cup increase if the height of the starting position of the ball was doubled? Quadrupled?
mgh = mv2 The mass values cancel
gh = v2
v = (2gh) 2g is a constant and wont be affected by a change in h, therefore we can disregard it.
So v is dependent on h as follows:
v = (h)
When h is doubled, v = (2h) so v increases by a factor of (2).
When h is quadrupled v = (4h) so v increases by a factor of 2.
How could you decrease the distance the cup travels? How could you increase it?
I could decrease the distance the cup travels by making the ramp lower. If the ball started rolling at a lower position, it would have less energy when it hit the cup. The result would be that the force of friction would have to do less work on the cup to bring it to rest. Since the mass of the ball and the coefficient of kinetic friction remain constant, the force due to friction will also remain constant. So the only way less work will be done is if the mass does not move as far. Increasing the height of the ramp would have the opposite effect and the cup would travel farther. Note: An increase or decrease in the mass of the ball would affect energy and the frictional force so the cup would move the same distance. The only case when this isnt true is if the ball is so light that it doesnt hit the cup with a strong enough force to overcome static friction.
As an engineer, how would the knowledge of how to find the coefficient of friction between two materials be helpful when designing a roller coaster?
If I were designing a roller coaster, I would have to know what the coefficient of friction between the wheels and the track is. Knowing what the coefficient of friction is would determine how fast the roller coaster can go and whether or not I would have to make an incline for turns. I would need to make sure that it does not go so fast that the wheels come off the track during a turn.
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