Physics 170. Midterm III
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There are 4 problems. Each is assigned 25 points.
Show your work.
Problem 1: 25 points
A solid ball of mass M and radius R starts from rest and rolls without slipping down a hill. Its center of mass drops a total distance h.
(a) Find the ball's speed at the bottom of the hill
in terms of M, R, and h.
(Note that the moment of inertia of a sphere
around an axis through a diameter is 
).
Problem 2: 25 points
The figure below shows how a scale with a capacity of only 250 N can be used to weigh a heavier sumo wrestler. The board is 3.0 m long, has a mass of 3.4 kg, and is of uniform density. It is free to pivot about the end farthest from the scale. The scale reads 210 N.
(a) Identify the forces in the problem.
(b) What is the weight of the wrestler ?
(c) (Extra credit, 1 point). Who is this sumo wrestler ?
Problem 3: 25 points
A spherical shell has a radius of 2 m and a mass of 200 kg and its
center is located at the origin of the coordinate system. Another
spherical shell with a radius of 0.5 m and a mass of 100 kg is inside the
larger shell. The center of the smaller spherical shell is located
0.5 m from the origin and lies on the x axis.
(Note 
N-m 
/kg )
(a) What is the gravitational force on a test particle (mass=1 kg), located on the x-axis, 1.5 meters from the origin of the coordinate system ?
(b) What is the gravitational force on a test particle (mass=1 kg) at the center of the smaller spherical shell ?
Problem 4: 25 points
Physicists have developed amazing new materials called aerogels
that are at once amazingly light and yet surprisingly strong.
A particular cube of aerogel is made from 1.00 gram of silicon dioxide.
Yet its apparent weight on a scale is only 
N.
What is the ratio of
the density of aerogel to the density of air
(i.e. find 
)?