1. If a penny is dropped from the top of the Empire State Building, how fast is the penny traveling when it reaches the ground if there were no air resistance?
a. Empire State Building is 443 m from the sidewalk to the highest point. Mass of a penny is 0.0025 kg. Determine the Potential NRG of the penny when it is at the very top of the Empire State Building.
b. Determine the Kinetic NRG of the penny when it is starting at the top of the Empire State Building.
c. What is the Total Mechanical NRG (TME) of the penny?
d. What will be the Potential NRG of the penny when it has reached the sidewalk?
e. What is the Kinetic NRG of penny the millisecond before impacting the ground?
f. How fast will the penny be traveling at the point in time for part e?
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2. The Birds have been working on ways to launch themselves at even higher speeds. They have built an Air Cannon and want to see how high they can go. They have determined that the Air Cannon can accelerate a Bird to a speed of 24.6 m/s. a. Red Bird decides to be the test tweeter. He has a mass of 0.01 kg. Determine the Kinetic NRG Red Bird will have upon leaving the Air Cannon with a speed of 24.6 m/s.
b. If the end of the Air Cannon is a height of 0.0m, what Potential NRG will Red Bird have at this point?
c. What will be the TME for Red Bird when he exits the end of the Air Cannon?
d. When Red Bird Reaches the highest point, what will be his TME?
e. When Red Bird Reaches the highest point, what will be his Kinetic NRG?
f. When Red Bird Reaches the highest point, what will be his Potential NRG?
g. Using the Potential NRG of Red Bird at the highest point, determine how high he will reach above the end of the Air Cannon. (Will he enter into space and become a Space Bird?)
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3. The Pigs have captured some Eggs and are escaping in a balloon. Red Bird is going to stop the Pigs from getting away by launching himself straight up into air and at the Pigs. The balloon stops rising and reaches a height of 80m.
a. The Red Bird has a mass of 0.01kg. When the Red Bird reaches the balloon, what Potential NRG will he have?
b. If the Red Bird just reaches the balloon, what will his Kinetic NRG be at the height of the balloon?
c. What is the TME for Red Bird at the height of the balloon?
d. What will be the TME for Red Bird when he starts out at ground level?
e. What Potential NRG does the Red Bird have when he is at ground level?
f. What Kinetic NRG will Red Bird have when he begins his rescue mission?
g. How fast must Red Bird be traveling at ground level in order to reach the balloon?
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4. Jerry is trying to make it home without waking up his parents. His house is at the top of a hill that is 50m above the level of the road and the driveway is at a very shallow angle. To make it home without waking his parents, Jerry will need to turn off the engine of his car at the bottom of the hill and coast to the top. Jerry and the car have a combined mass of 800 kg.
a. Draw a diagram of the situation. Include the measurements given and the data supplied.
b. Use the given information to determine the Potential NRG Jerry will have at the top of the hill.
c. How much Kinetic NRG will Jerry need at the bottom of the hill to make it to the top?
d. Determine how fast Jerry must be going at the bottom of the hill to just make it to the top and stop if there is no friction present.
e. What Force is doing work on Jerry as he coasts up the hill?
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5. How can we use NRG relationships to pull off an extreme stunt?
Lenny decides to tie a 30m long rope to the bottom of a bridge and use the rope to swing underneath the bridge. Lenny has a mass of 80.0 kg and starts from the edge of the bridge with the rope fully stretched out when he starts.
a. How high above the lowest point of the swing does Lenny start?
b. What is the Potential NRG for Lenny at the starting point of his swing?
c. What is the Kinetic NRG for Lenny at the starting point?
d. What is the Total Mechanical NRG of the system?
e. What will be Lenny’s Potential NRG at the lowest point of the path he follows when on the swing?
f. What will be Lenny’s Kinetic NRG at the Lowest Point of the path he follows when on the swing? 5
6. Finding the speed of a roller coaster car.
A kiddie Roller Coaster is being built. The ride has the car start from rest at the top of a 18.75m tall hill. The car then goes down the track and enters into a teardrop shaped loop. The highest point on the loop is 15m above the ground.
a. What is the Kinetic NRG of the Roller Coaster car at the top of the start hill?
b. If the Roller Coaster car has a mass of 200 kg, determine the Potential NRG the car has at the starting point.
c. What is the TME of the car at the starting point?
d. What is the TME of the car at the highest point of the loop?
e. What is the Potential NRG of the car at the highest point of the loop?
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