IB Physics HL
Lab exploring Mechanics
The Ramp and Loop
Aim: Prove that the height of a ramp must be at least 2.5 times greater than the height of a loop for an object to overcome gravity.
Question: In theory, the height of a ramp must be at least 2.5 times greater than the height of a loop for an object to be able to overcome gravity and remain on its path. Will this happen experimentally?
Background: The following derivation demonstrates that ideally the height of the track initially (h2) will equal to 2.5 times the radius of the loop.
U = mgh1 = 2mgR
2mgR = 2mv2(top)
ET = U + EK
ET = 2mgR +
ET = 2mgR +
ET = 2
mgh2 = 2
h2 = 2
Hypothesis: The radius of the loop must be 2.5 times smaller than the height of the ramp through which it must first fall.
Independent: The size of the radius of the loop is what will be increased in the experiment; in the derivation demonstrated earlier the variable that would be changed is R. This will directly influence the height needed for the ball overcome the loop.
Dependent: The height of the initial fall of the ramp is what would be changed as a result in the change of the radius of the loop because more kinetic energy must be gained by the ball so that it doesn't fall while on the ramp; in the derivation demonstrated earlier the variable that would be changed is h2.
Control: The mass of the ball used in the experiment will remain the same since only one ball will be used throughout. The height needed is not a function ofthe mass, but if the mass is changed, there might be a discrepancy in the values due to different amounts of friction. Also, the friction with the tracks will remain the same since the same kind of tracks will be used throughout. The change in friction requires that more height be used, so that the kinetic energy of the ball is greater than the force due to gravity in the loop in addition to the force due to friction.
Hot-wheels base for loops
Table or chair (at least 70 cm in height)
Tape the meter stick to the table or chair to measure the initial height of the ball.
Connect smaller tracks to make a longer track of about 80cm.
Tape one end to the top of the chair or table and connect the other end to the hot-wheels base for loops.
Tape the base to the ground.
For each trial, the number and size of the tracks connected to the base to form the loop will need to be changed. (Suggested values for the radii of the loop are 8.75cm, 11.5cm, 13.5cm, and 15.25cm.) See figure 1 for reference.
Place the metal ball at 2.5 times the radius of the loop on the height of the initial ramp. Let go and annotate whether or not the ball completes the loop.
Then follow the same procedure,...