Mechanical Energy I. Name: Date: Section C D F. Mr. Alex Rawson Physics

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1 Name: Date: Section C D F Mechanical Energy I Mr. Alex Rawson Physics 1. One of the two Olympic weightlifting events is called the Clean and Jerk, shown below. As of Athens 2004, the record for Clean and Jerk is kg (578.7 pounds). a. What is the change in potential energy of this exercise if the weights are lifted 2.2 meters? b. What would the change in potential energy be on the moon, where the acceleration of gravity is 1/6 th that of Earth s? 2. A 185 g particle is released from rest at point A inside a smooth hemispherical bowl of radius 25.0 cm, as shown in the figure to the right. a. Calculate the gravitational potential energy at A relative to B. b. Calculate the particle's kinetic energy at B. c. Calculate the particle's speed at B. d. Calculate the kinetic energy and potential energy at C. 3.

2 A child and sled with a combined mass of 40.0 kg slide down a frictionless hill. If the sled starts from rest and has a speed of 12.0 m/s at the bottom, what is the height of the hill? (Remember that energy is conserved here) 4. Tarzan swings on a 35.0 m long vine initially inclined at an angle of 37.0 with the vertical. What is his speed at the bottom of the swing if he starts from rest?

3 Name: Date: Section C D F Mechanical Energy II Mr. Alex Rawson Physics 1. Tarzan swings on a 20.0 m long vine initially inclined at an angle of 44.0 with the vertical. What is his speed at the bottom of the swing if he does the following? a. He starts from rest. b. He pushes off with a speed of 4.00 m/s. 2. Tarzan and Jane, whose total mass is kg, start their swing (at rest) on a 34.0 m long vine when the vine is at an angle of 25.0 with the horizontal. At the bottom of the arc, Jane, whose mass is 50.0 kg, releases and jumps off. If Tarzan holds on to the vine, and rises on the other side of the pendulum swing, what is the maximum height at which Tarzan can land on a branch? (Hint: Find the velocity at the bottom, then find the height Tarzan can gain with that velocity)

4 3. A 45.0 kg pole vaulter, attempting her personal best height, runs at 9.0 m/s towards the high bar. Assuming that she succeeds, and at the peak of her vault she retains a horizontal velocity of 1.2 m/s over the bar, how high was the bar? 4. How high would a.2 kg block rise if it were aligned on a vertical 5.00 x 10 3 N/m spring, and someone pushed downward on the block compressing the spring m? KE i + PE i,grav + PE i,elastic = KE f + PE f,grav + PE f,elastic ½mv i 2 + mgh i + ½kx 2 i = ½mv f mgh f + ½kx f PE i,elastic = PE f,grav ½kx 2 i = mgh f

5 Name: Date: Section C D F Mechanical Energy III Mr. Alex Rawson Physics 1. A ski jumper starts from rest 50 m above the ground on a frictionless track, and flies off the track at a 45 o angle above the horizontal. If the track launch is at a height of 10 m from the ground: a. What is the skier s speed when leaving the track? b. What is the maximum height attained in mid-air relative to the ground? 2. A 25 kg child on a 2.0 m long swing is released from rest when the swing supports make an angle of 30 o with the vertical. a. What is the child s total mechanical energy? b. Disregarding friction, find the child s speed at the lowest position. c. If the speed of the child at the lowest position is 2.0 m/s, what is the mechanical energy lost due to friction? (disregarding friction) ME i = ME f 3. (with friction) ME i W friction = ME f Mechanical Energy = KE + PE grav + PE elastic KE i + PE i W friction = KE f + PE f PE i W friction = KE f PE i KE f = W friction

6 A skier starts from the top of an icy 7.34 m hill, and gains speed down the hill without any friction. Once the skier reaches the bottom, the snow is heavier, and creates a coefficient of kinetic friction of.08. a. How fast was the skier going at the bottom of the hill? b. How far would the skier go horizontally before coming to a full stop? (with friction) ME i W friction = ME f KE i + PE i W friction = KE f + PE f KE i W friction = 0 KE i = W friction

7 Name: Date: Section C D F Power Mr. Alex Rawson Physics 1. What is the top speed that a boat could travel in rough water, if it has a 200 hp outboard motor, and the water exerts a resistive force of 8300 N? 2. If a V-12, 1700 kg Lamborghini Diablo can accelerate from rest to 60 mph (26.82 m/s) in 3.2 seconds, with an average of 1.8 x 10 4 N resistive force, how much horsepower does the Lamborghini Diablo have under the hood? 3.

8 For wakeboarding enthusiasts who may not have a boat, they have to resort to something called a winch, which is a makeshift tow rope that can pull a wake boarder by engine power alone. The best winch around is called The Grinch Winch (give it a search on Youtube), a 7 hp winch with 600 m tow rope. a. How fast would you be riding if you were pulled by the winch with a 400 N force? b. How long would the ride be?