EXAM 2 October 29, 1997 PHYS 207
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No notes, books, etc. may be used during this exam.
| g = 9.8 m/sec2 | Radius of the earth = 6.38 x 106 m |
The mass of the electron is 9.11 x 10-31 kg. |
For all problems, place the equations representing the physics
principles you are using in the box on the page. You may use the
general form of the equation or the form you get applying the
principle to the problem at hand. If no diagram is applicable to
a problem, write "none" in the diagram section.
1. (a) (5 points) You want to measure the kinetic energy of a cart on
an air track and you have apparatus that allows you to measure its
mass and velocity, and you can repeat those measurements as many times
as your patience allows. The accuracy of your apparatus is such that
sigmam /m = sigmav /v.
In each case sigma refers to the standard deviation of the
distribution of single measurements of the quantity. You want your
uncertainty in the value of the mass and your uncertainty in the
measurement of the velocity to make equal contributions to the
fractional uncertainty of the kinetic energy. What must be the ratio
of the number of times you measure the mass to the number of times you
measure the velocity? Justify your answer.
(b) (5 points)
Show how to remember the functional dependence of the spring potential
energy
Usp = (1/2) K (delta x)2
on delta x, where
Fsp = - K delta x.
2. (30 points)
A trunk of mass m is pushed a distance d at a
constant speed of v up a frictionless incline of angle
theta by a horizontal force F. Calculate the work done
on the trunk by (a) the applied force F, and (b) the
gravitational force.
Diagram:
Principles:
3. (From homework, 30 points)
A boy is seated on the top of a hemispherical mound of ice, similarly
to the block shown in the figure to the left. He is given a very
small push and starts sliding down the ice. Show that he leaves the
ice at a point whose height is 2R/3 if the ice is frictionless.
Diagram [or you may add to the diagram above]:
Principles:
4. (30 points) A 3 kg block is pushed against a spring of spring constant
50 N/m, compressing the spring by 2 m. The block is released and the
spring accelerates it across a frictionless surface. When the spring
reaches its equilibrium position, the block slides along a surface
whose coefficient of kinetic friction is 0.2. How long does it take
for the block to come to rest?
Diagram:
Principles:
Use this page if necessary to continue any of the problems. Be sure to
label the problem number.