1. Students in a physics class placed two objects on the top of a ramp as shown
ID: 1873127 • Letter: 1
Question
1. Students in a physics class placed two objects on the top of a ramp as shown in the diagrams above. The ramp has a small rise at the end which causes objects to be launched upwards at a small angle. First the students placed a block of ice (which has no friction with the ramp’s surface) at the top of the ramp and released it. Next, the students placed a thin hoop at the top of the ramp and released it.
a) Which of the two objects, if either, reaches a greater height after leaving the ramp? Justify your answer qualitatively without any equations.
b) Which, if either, would reach a greater height if the hoop was also made of ice and slid down the ramp without rolling? Justify your answer qualitatively without any equations.
c) Suppose the final angle of the ramp is 30º. How can the maximum height of each be determined?
Africtionless block of ice with m ass, m slides down the ramp from rest. ML A thin hoop m ass, m, andra dius,r, rolls down the rampfrom rest without slippingExplanation / Answer
a. in the given figures, both the objects have the same mass and are released from the same initial height
but when they come down even though they have lost the same anount of PE, the have not gained the same ampount of translational KE
The ice block on one hand has all its PE concerted to Translational KE
the rolling hoop has its PE divided into Tranlational KE and rotational KE
hence
the rolling hoop has less linear speed at the enfd of the incline and the ice block reaches greater height after jumping off from the end of the incline
b. if the hoop slid down, and did not rotate, then it will too reach the same height as the ice block
c. angle of ramp = theta
hence
final height = h
initial height = H
from conservation of energy
mgH = 0.5mv^2*cos^2(30) + mgh
and mgH = 0.5mv^2
hecne
mgH = mgH*cos^2(30) + mgh
h = mgH*sin^2(30) = mgH/4
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