. 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?
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.
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?

1. Consider a modified Atwood machine, with a mass sitting on an inclined plane connected by a string which stretches over a pulley connected to a hanging mass. See picture. Friction is ignored.
a) Draw a free body diagram for both block 1 and block 2. b) Apply Newton’s second law to both block 1 and block 2. c) If the angle is 30o, and the mass of block 2 is 10 kg while the mass of block 1 is 15 kg, find the tension in the rope.
2. Consider the following system with a 2 kg mass sitting on a table, connected to both 1 kg and 3 kg masses by strings which go over two separate pulleys and are pulling on the 2 kg mass in opposite directions.
a) What static friction coefficient would be required between the 2 kg mass and the table to stop the masses from accelerating? b) If the masses are in motion, what kinetic friction coefficient would be required between the 2 kg mass and the table to ensure the masses move at a constant velocity? c) Find the tension in both pieces of string for the case of zero friction.
3. 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. For now, we are going to assume energy is conserved and ignore momentum. (We’ll come back to this problem later!)
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 to rescue Jane?

1. Here are the densities and radii of planets in our solar system (in grams per cm3 and km, respectively)
Mercury 5.4 g cm-3 2,440 km Venus 5.2 g cm-3 6,052 km Earth 5.5 g cm-3 6,378 km Mars 3.9 g cm-3 3,396 km Jupiter 1.3 g cm-3 71,492 km Saturn 0.7 g cm-3 60,268 km Uranus 1.3 g cm-3 25,559 km Neptune 1.6 g cm-3 24,764 km
How much would you weigh on these different planets? 1 pound is equal to 0.453592 kg.
2. Consider an Atwood’s machine consisting of two masses connected by a string which is over a pulley, as shown in the picture.
a) Draw a free body diagram for both block A and block B. b) Apply Newton’s second law to both block A and block B. c) the mass of block A is 14 kg while the mass of block B is 6 kg, find the tension in the rope.
3. Consider a modified Atwood machine, with a mass sitting on a table connected by a string which stretches over a pulley connected to a hanging mass. Friction is ignored.
a) Draw a free body diagram for both block 1 and block 2. b) Apply Newton’s second law to both block 1 and block 2. c) If the mass of block 2 is 20 kg while the mass of block 1 is 5 kg, find the tension in the rope.