Assignment:
1. Now you've covered momentum lets look again at last weeks question. Tarzan is running towards a cliff, ready to swing down, rescue Jane from some poisonous snakes, and make it back up to a tree on the other side. Now we must remember that energy isn't conserved in the collision (of course it is, but some of the energy is lost as heat, sound, etc... so its not recoverable), but momentum is!
If the height of the cliff is 10 m, the height of the tree on which Tarzan hopes to land is 7 m, the mass of Tarzan is 100 kg and the mass of Jane is 50 kg. What velocity does Tarzan have to be running at to rescue Jane?
2. You are in a small boat in a swimming pool and have a brick also in the boat with you. You throw the brick overboard and into the swimming pool. Does the level of the water in the swimming pool rise, stay the same or decrease? Show calculations to back up your answer!
3. In the olden days we used to have milk in bottles delivered by the milkman. The cream would rise to the top of the bottom, and occasionally a bird would come along and peck at the top of the bottle to get at the cream! Compare the milk bottle where the cream is still uniformly mixed with the milk, to the same milk bottle later on when the cream has separated and risen to the top. Does the hydrostatic pressure at the bottom of the milk bottle remain the same during the phase separation of the cream?
4. Its raining and your trying to decide whether or not to run or walk. If you walk you'll spend longer in the rain, but if you run you'll be running into the rain and potentially get wetter. The rain is falling with a velocity of which has both an x-component as it blows sideways and a y-component as it falls.
You move with a velocity of which only has an x-direction. If the rain is falling with a density and you have a top area of (which rain will fall onto) and a sideways area of (which rain will fall onto if it blows sideways or you move sideways into it), find an expression for how wet you
would be when traveling a distance d, as a function of your velocity.
5. The range equation can only be used if the projectile is launched from the ground and returns to the same height as it was fired from. What if instead it was fired from a given height, h?
a) Find the range of an object fired from a height h and at an angle .
b) Find the angle of launch which maximizes the range as a function of height.
6. A skateboarder in a death-defying stunt decides to launch herself from a ramp on a hill. The skateboarder leaves the ramp at a height of 1.4 m above the slope, traveling 15 m s-1 and at an angle of 40o to the horizontal. The slope is inclined at 45o to the horizontal.
a) How far down the slope does the skateboarder land?
b) How long is the skateboarder in the air?
c) With what velocity does the skateboarder land on the slope?
7. A car is driving around a bank curve such that it can safely go around a circular curve at a given velocity, vo, even when on ice (zero friction). Any slower and the car would slide down towards the center of the circle, any faster and the car would slide up the hill and away from the center of the circle. If a static frictional coefficient, , is introduced then the car can safely navigate around the curve at any speed between a minimum speed of vmin and a maximum speed of vmax. Can you find expressions for vmin and vmax as a function of vo, and the radius of the road, R.
8. In the system shown three masses are connected via string and a series of pulleys to one another.
Find the acceleration of all blocks.
Do not assume the slope to be frictionless, but assume that block A is in motion.
9. In a cardiac stress test the patient is required to walk on an inclined treadmill. Imagine that the patients mass is 80 kg and that the inclined treadmill is at a slope of 15o. The efficiency of the human body can be taken to be 25%.
a) Obtain an expression for the power required by the patient to maintain a velocity of 3 m s-1.
b) How long would the patient have to walk on the treadmill to burn the energy contained in a bottle of beer, a slice of pizza and a jelly doughnut?
10. A 1 kg block of wood is moving with a velocity of 10 m s-1 on top of a table. The coefficient of kinetic friction between the block of wood and the table is 0.1. The block of wood is a cube with sides of 12 cm.
a) How far does the block move before coming to a stop?
b) If momentum id conserved, where did the momentum of the block go?
c) The block slows down because of the frictional force between the block and the block. However, if the frictional force acts at the bottom of the block and the blocks center of mass is in the center of the block then there must be a torque acting on the block. Calculate this torque. Why doesn't this torque cause the block to rotate?