Name ______
UConn 1201 Final Exam Fall 2009
Instructions: -1010 School Year
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?
(c)(b)
(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, (distance d), does the car go once the skid has begunskid 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 50.0 N beam.The beam is supported by the attached guy wire, tilted at 37° deg 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?
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? 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 b y 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. Show that these solutions make good sense based on everyday experience considering collisions between a small ball bearing and a bowling ball, and someone playing pool who knocks a ball directly into the side pocket using the cue ball. The only difficult case to interpret may be C, but it helps to imagine an observer moving along with m1 in this case.
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 as 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 ?
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. 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 rower land?
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:
- m2 > m1
- m2 = m1
- 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.
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 degrees C to melt in the cooler if the outside temperature is 30 deg C? The thermal conductivity of Styrofoam is 0.030 W/m Deg 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 degrees C until all the ice is melted.
10. A scheme for running a cyclic engine is based on the thermal gradient between deep ocean water and water near the surface. Assume the surface water is at temperature 22 0 C and the deep water is 15 0 C less than the surface water. What is the maximum possible thermal efficiency of such an engine?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?