The muzzle velocity of a ball bearing was calculated through an experiment (1.22m/s). A student then wants to verify that the velocity calculated is right. So, she conducts an experiment in which she points the ball bearing launcher upwards. She measures the height the ball bearing climbs before falling back to the table.
1. What height is expected that the ball bearing reach.
I used the formula: vf=vo+2ax (velocity as a function of displacement)
so... 1.22^2=0+2(9.8)x, x = .0759m
2. For a given velocity, does the height depend on the mass of the ball?
According to the last problem, (if I did it right), the height does not depend on the mass.
Am I correct? Your help would be greatly appreciated.
you are correct on both, however, on the first you worked it with a sign problem. Gravity is down, so it should have been negative, and you put in Vf, not Vo.
Should have been
Vf^2=Vo^2 + 2ad
0=1.22^2 + 2(-9.8)x
1. To calculate the expected height that the ball bearing will reach, you can use the formula vf^2 = vo^2 + 2ax, where vf is the final velocity (which is zero when the ball bearing reaches its maximum height), vo is the initial velocity (muzzle velocity), a is the acceleration due to gravity (approximately 9.8 m/s^2), and x is the displacement.
So, you correctly used this formula and solved for x: 1.22^2 = 0 + 2(9.8)x. By solving for x, you found that x = 0.0759 m.
Therefore, the expected height that the ball bearing will reach when launched upwards is approximately 0.0759 meters.
2. You are correct! The height that the ball bearing reaches does not depend on the mass of the ball bearing. In this scenario, the height is only affected by the initial velocity and the acceleration due to gravity. The mass of the ball bearing does not play a role in determining the height.
So, whether the ball bearing is heavy or light, it will reach the same height when launched with the same initial velocity.