Name _____________________
UConn 1201 Final Exam Fall 2009
Instructions: Choose 8 of the following problems to be graded. You may have your formula sheet.
The Problems that I choose NOT to be graded are _____&_____
1. An arrow is shot with a velocity of 30 m/sec at an angle of 37 deg. above the horizontal. The
arrow is initially 2 m above the ground and 15 m away from a tall vertical wall.
(a) When the arrow strikes the wall, is its vertical component of velocity pointing up or down?
(show how you know this)
(b) How high above the ground does the arrow strike the wall?
(You can neglect the issue of whether the front or back of the arrow might strike the wall at
different heights, assume the arrow is short enough you can neglect this effect.)
2. A car of weight, (W), travels in a straight line, along a level road, suddenly applies its brakes. A
short time after the brakes are applied the tires stop turning and go into a skid. The skidding tires
continue to go in a straight line and experience a frictional force from the road of 0.7 (W). How far,
(d), does the car skid in coming to a stop? Assume the velocity of the car at the moment the wheels
began to skid was V. Obtain the distance, (d), in terms of the other known quantities, that may include
(V),(W), and (g).
3. As illustrated in the diagram below, a 100 N weight is on the end of a 50 N beam. The beam is
supported by the attached guy wire, tilted at 37° relative to the horizontal, and a hinge which is
fastened to the wall.
What are the x (horizontal) and y ( vertical) components of the force of the hinge on the beam?
100 N
37 º
100 cm
40 cm
4. A person, who can row a boat at 5.0 km/hr in still water, tries to cross a river whose current moves
at a rate of 3.0 km/hr. The boat is pointed straight across the river (perpendicular to the current
direction). If the river is 200 m wide how far downstream, from the original departure point, does the
boat make landfall on the other side of the river?
5. The most massive concrete block you can carry on land is 25 kg. If you were in a diving suit
carrying a 25 kg block under water, how much would it seem to weigh to you? The density of concrete
is 2.3 x 103 kg/m3 and the density of water is 1.0 x 103 kg/m3 .
6. Assume the earth’s orbit around the sun is circular and that the radius of this circle is 150 x 106
km. Assume the mass of the sun is 1.99 x 1030 kg, and that G = 6.67 x 10-11 Nm2/ kg2 .
Derive an expression for the period of the earth in its orbit in seconds, and check this against the value
you know.
7. Suppose the roller coaster car shown below starts, from rest at point A, and moves without friction.
a) How fast is it moving at points B, C, and D?
b) What constant negative acceleration must be applied at D to have the car stop at E, which is a
horizontal distance of 30 meters to the right of D as shown?
A
C
10 m
D
B
6m
E
30 m
5m
3m
8. A Styrofoam cooler has a surface area of 0.50 m3 and an average thickness of 2.0 cm. How many
hours will it take 1.5 kg of ice at zero ºC to melt, in the cooler, if the outside temperature is 30 ºC? The
thermal conductivity of Styrofoam is 0.030 W/m•C, and the latent heat of melting of ice is 3.34 x 105
J/ kg. Make the assumption that the inside temperature is zero º C until all the ice is melted.
9. Let a spherical object with mass m1 have positive initial velocity along the horizontal x direction of
V1i . A particle of mass m2 is initially motionless and is struck dead center by m1 in an elastic
collision. All motions in this problem are one dimensional, and lie along the x axis.
With some messy algebra it can be shown that the final velocities of m2 and m1 are given by the
following expressions, respectively:
(a) V2f = [2m1 / (m1 + m2 )] V1i
(b) V1f = [(m1 - m2 ) / (m1 + m2 )] V1i
Consider the following special cases:
A. m2 >> m1
B. m2 = m1
C. m2 << m1
Find specific expressions for the final velocities of both particles for cases A, B, and C. Describe
what happened in each of these solutions using your experience of colliding objects.
10. A 64 g sample of O2 gas is held at 25 C and 2 atm of pressure.
a. Find the volume that this gas occupies in liters.
b. The RMS velocity of the Oxygen molecules
c. If this gas is isothermally expanded to twice it’s original volume, what will happen to the speed of
the molecules?