PHY 1151
Summer 2003
Third Hour Exam
July 2, 2003

Statistics

High: 100 (2!!)

Mean: 84

Low: 40

BRAVO! I was very pleased with your results on this test. You did a good job!

 

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1. Consider a solid disk suspended as shown in the sketch here. The solid disk has a mass of 4 kg and a radius of 0.1 m. Therefore, its moment of inertia (or “rotational mass”) is

I = (1/2) M r2 = (1/2) (4 kg) (0.1 m)2
I = 0.02 kg m2

A 2 kg mass is suspended from a string or cord that is wrapped around the solid disk as shown here. The solid disk rotates as the cord unwinds so there is no slipping between the disk and the cord.

What is the acceleration of the hanging mass?

2. A 10-cm cube of wood floats in water with 2 cm above the water and 8 cm below the water (as shown in the sketch here). What is the density of the wood?

(H2O) = 1000 kg/m3

3. Water flows through a horizontal pipe that changes area from 25 cm2 to 15 cm2. In the 15 cm2 region, the flow velocity is 5.0 m/s.
a) What is the flow velocity in the 25 cm2 region?
b) What is the pressure difference between the two regions?

(H2O) = 1000 kg/m3


4. Consider a steel wire, 1.000 m long and 0.5 mm in radius. How much does is stretch when a weight of 200 N is suspended from it?
Young’s modulus for steel is Y = 20 x 1010 N/m2 .

Concept Questions:

i. Think of a diver doing a double sommersault. He leaves the diving board hardly rotating at all. During most of his fall, he pulls his arms and legs in and spins very quickly. Before he enters the water, tho’, he extends his body and greatly slows his rotation to make an elegant and graceful entry into the water. Explain what happens in terms of the physics principles we have discussed recently.

Angular momentum is conserved. Angular momentum is the product of moment of inertia multiplied by angular velocity. Initially outstretched, the diver has a large moment of inertia. As he pulls himself into a “tuck” position, his moment of inertia become small and that requires that his angular velocity becomes large. Before entering the water, he extends his body and that makes his moment of inertia large. A large moment of inertia requires a small angular velcoity.


ii. A solid disk and an open hoop are released from the same height on an inclined plane. Which reaches the bottom first? And why?

The solid disk has a smaller moment of inertia. That means it is easier to rotate so it comes down the inclined plane faster — and first!


iii. Why do people commonly refer to the weight of a ship as its “displacement”?

The bouyant force provided by the water is equal to the weight of the water displaced by the ship.


iv. As air moves across the top of a chimney, will air be pushed down into the chimney and into the house or will air be pulled from the house and up and out of the chimney. Why?

From Bernoulli’s equation, we know that the pressure of a moving fluid is less than the pressure of the fluid at rest. Thus the air pressure at the top of the chimney, where the air is moving, is less that the air pressure inside the house, at the fireplace. Therefore, air will move from inside the house, through the fireplace, up the chimney, and out into the moving air.

 

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