Problem 7: h, 5. (15 7. (12 points) A daredevil rides a go-cart, first down a hi
ID: 1789245 • Letter: P
Question
Problem 7: h, 5. (15 7. (12 points) A daredevil rides a go-cart, first down a hill and then he makes a jump using a ramp (as depicted above). The hill has an elevation of h, 20 m high. Take the mass of the go-cart plus daredevil to be 200 kg. At the top of his jump the daredevil is travelling at 10 m/s. (Assume that the go-cart does not provide any acceleration and that there is no friction or air resistance, thus the only relevant force in the problem is gravity.) (a) (6 points) Determine the daredevil's kinetic energy at the bottom of the ramp. (b) (6 points) Determine the daredevil's potential energy at the maximum height of the jump, with the assumption that the potential energy at the top of the hill is zero. (Note that when an object is below the zero of elevation, its height is negative.)Explanation / Answer
a.) By the law of conservation of energy, we say that
The increase in Kinetic energy should be equal to the decrease in potential energy
Since the initial kinetic energy at the top of the hill is zero, the kinetic energy at the bottom is nothing but the drop in the potential energy as the daredevil - cart system falls through the ramp , which is Mghi = 200 x 9.8 x 20 = 39200 J
b.) At the highest point of the jump, the speed of the cart is 10 m/s, which means the Kinetic energy at that point is
KEf = 0.5Mv2 = 0.5 x 200 x 102 = 10000 J
Now, if the top of the hill is taken as a reference, the initial Potential energy is 0. Also, the initial Kinetic energy at the top of the hill is also 0, since the speed was zero at the top of the hill.
By the law of conservation of energy, the total energy which is the sum of Kinetic and Potential energies remains constant throughout in the absence of a non-conservative force. So,
PEi + KEi = PEf +KEf
0 + 0 = PEf + 10000
PEf = - 10000 J