Physics 131-01 Test 3
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Questions (8 pts. apiece) Answer in complete, well-written sentences WITHIN the spaces provided.
- Suppose a ball of mass 0.20 kg is dropped and falls toward the surface of
the moon so that it hits the ground with a speed of 40 m/s and rebounds with
the same speed. Consider the ball and the moon as an interacting system with no other outside
forces. Why might the astronaut (who hasn't taken physics yet!) have the illusion
that momentum isn't conserved in the interaction between the ball and the moon?
- Using the diagram below, draw a dotted line in the direction you think your
two cars will move after a perfectly elastic collision between cars with different masses and
the same velocities.
Explain your reasoning in the space below.
- Assume that an object is moving in a circle of constant radius,
and recall that
where
is the arc length along the edge of a circle,
is the radius
of the circle, and
the angle.
Take the derivative of
with respect to time to find the velocity of the object.
Show that the magnitude of the linear velocity,
, is related to the magnitude of the angular velocity,
, by the equation
.
- Recall the laboratory where you studied a rotational collision. You dropped from rest a weight onto
a spinning rotator and measured the motion before and after dropping the weight from rest to test the
conservation of angular momentum.
Would the procedure you followed change if the weight was moving horizontally at a constant velocity
when you dropped it?
If it changed, what would be different?
- As global warming continues over the next century, some of the polar ice fields
will melt and more water will end up near the equator.
How would this change the moment of inertia of the Earth?
Would the length of a day increase or decrease?
Explain.
Problems. Clearly show all reasoning for full credit.
Use a separate sheet to show your work.
Problems. Clearly show all reasoning for full credit.
Use a separate sheet to show your work.
2. |
20 pts. |
Measuring the moment of inertia of an irregularly-shaped object like the payload of a spacecraft
can be done with a device like the one shown in the figure.
A counterweight of mass is suspended by a cord wound around a spool of radius , forming part of a
turntable supporting the object.
The turntable can rotate without friction.
When the counterweight is released from rest, it descends a distance , acquiring a speed .
Show that the moment of inertia of the rotating apparatus including the turntable is
.
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3. |
25 pts. |
A widely accepted theory of planet formation states that planets form out of dust that collides and sticks to form larger and larger bodies.
When two of these `planetesimals' hit they can coalesce and form (through melting from the heat released in the collision) a single, spherical object.
A non-spinning planetesimal of mass and radius is moving with velocity to the right as shown in the figure below.
It collides with an identical (same and ), non-spinning planetesimal moving to the left with velocity and they stick together.
The velocities are parallel, but in opposite directions.
Their initial trajectories are a perpendicular distance apart as shown in the figure.
They eventually form a uniform spherical body with mass and radius .
What is the velocity of the final object after the collision in terms of the information given above ( , , , , and )?
What is its angular velocity after the collision in terms of the same information?
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Physics 131-1 Exam Sheet, Test 3
Speed of Light ( ) |
![$2.9979\times 10^8~m/s$](img41.png) |
proton/neutron mass |
![$1.67\times 10^{-27}~kg$](img42.png) |
![$R$](img43.png) |
![$8.31J/K-mole$](img44.png) |
![$g$](img45.png) |
![$9.8~m/s^2$](img46.png) |
Gravitation constant |
![$6.67 \times 10^{-11}~N-m^2/kg^2$](img47.png) |
Earth's radius |
![$6.37\times 10^6~m$](img48.png) |
Earth-Moon distance |
![$3.84\times 10^8~m$](img49.png) |
Electron mass |
![$9.11\times 10^{-31}~kg$](img50.png) |