Kinetic Work Theorem Physics

Kinetic Work Theorem: Work Changes an objects kinetic Energy. ∑ W = ΔK Total work = change in kinetic energy.

End velocity = initial velocity Bob vs. Friction Bob pushes a 2 kg crate for 5 meters. Friction resists with 10 N of force. What would happen if Bob pushed with the following three forces? Work Done by Bob: Work Done by Friction: Total Work: Change in Kinetic Energy: End Velocity: 10 N 30 N 5 N (30)(5) = 150 Nm (5)(5) = 25 Nm Bob’s force*crate Displacement (10)(5) = 50 Nm -(10)(5) = -50 Nm -(10)(5) = -50 Nm -(10)(5) = -50 Nm Friction*crate Displacement 50 – 50 = 0 Nm 150 – 50 = 100 Nm 25 – 50 = -25Nm WARNING: A change of 0 Joules does NOT mean the crate isn't moving. It means it didn't gain NEW speed. Friction stays the same and doesn’t change. What is changing is Bob’s pushing force. Increasing the force the final velocity is going to be greater. – (Demo this) Decreasing the force the final velocity is going to be less. – (Demo this) ∑ W = pos. work – neg. work 0 J 100 J -25 J End velocity = initial velocity vf > vo vf < vo

Gravity: It takes a great deal of work to get up a hill. Since work increases your kinetic energy, why aren’t you moving super fast at the top of the hill? Because gravity is taking it away. For example: My legs give me ____ J of motion… … but gravity takes away ____ J.

Bob vs. Gravity Bob (75 kg) is trying to get to the top of a 200 m tall hill.  How much work must Bob do to get there?  How much work will gravity do as Bob is climbing?  What is the TOTAL work done to Bob?  What was the change in kinetic energy?  What is the end velocity of Bob?

Skateboard Lab Field Trip!

Kinematics vs. Energy Bob turns on the engine to his 1500 kg boat, which provides 2500 N of force. He leaves the engine on for 450 meters. Meanwhile, water friction resists with 1900 N of force. Assuming that he started at rest, how fast will Bob be moving now?

Kinematics vs. Energy Bob tosses a 12 kg boulder off of a 125 m cliff. The average air resistance is 35 N of force. How fast will it be moving when it hits the ground?

More Practice Bob pulls an 11 kg wagon forward with 55 N of force at an upward angle of 52 degrees. The wagon moves 8 meters across the driveway. Meanwhile friction resists with 25 N of force. Assuming the wagon started from rest, how fast will it be moving now?

More Practice A 25,000 kg train was moving 18 m/s when it put on its brakes. If the brakes apply 2700 N of force, then how much distance will it take for the train to come to a complete stop?

More Practice A 500 kg rocket turns on its 8,000 N thrusters until it reaches an altitude of 250 m. Meanwhile the air resists with an average of 85 N. How fast will the rocket be moving now? (HINT: Don’t forget that gravity is doing work too. In this case it is negative work.)