# Kinetic energy – work theorem

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Kinetic energy – work theorem
Positive net work? Kinetic energy increases. negative net work? Kinetic energy decreases. Zero net work? Constant speed.

Average driving force of the biker?
A 90.0-kg biker (bike and person) approaches a 10-% hill at a speed of 10.0 m/s. After 60.0 m uphill, his speed is 4.00 m/s. Neglect friction. Work of gravity? Work of biker? Average driving force of the biker? L17sp09

A 50. 0-kg child drops off a ladder onto a thick spring mattress
A 50.0-kg child drops off a ladder onto a thick spring mattress. The top of the ladder is 2.50 m above the surface of the mattress. If the mattress springs have an effective force constant of 50 kN/m, what is the maximum depression of the mattress?

A particle starts from rest at x = 0 and moves to x = L under the action of a variable force F(x), which is shown in the figure. What is the particle's kinetic energy at x=L/2 and at x=L? a) Fmax L/2, FmaxL b) Fmax L/4, 0 c) Fmax L, 0 d) Fmax L/4, Fmax L/2 e) Fmax L/2, Fmax L/4

Two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. Gravity is doing work on them. Just before hitting the ground, the heavier marble has as much kinetic energy as the lighter one. twice as much kinetic energy as the lighter one. half as much kinetic energy as the lighter one. four times as much kinetic energy as the lighter one. impossible to determine

Power Rate of work output Constant force:

Example for Power calculations
A car is accelerating from 0 to 100 km/h in the time of 10 seconds. The mass of the car is 1000 kg. Assuming constant acceleration, determine the average power of the car engine the power the car engine has to expand at the end of the time interval.

A sports car accelerates from zero to 30 mph in 1.5 s.
How long does it take for it to accelerate from zero to 60 mph, assuming the power of the engine to be independent of velocity and neglecting friction? 2 sec 3 sec 4.5 sec 6 sec 9 sec 12 sec

Work of gravity Final position Final position Final position
Initial position Final position Initial position Final position Initial position Final position

Work of gravity Work is not dependent on path
Initial position Final position Initial position Final position Initial position Final position Work is not dependent on path Work is only dependent on initial and final position

Conservative Force The force of gravity is a conservative force.
The work of a conservative force is not dependent on path only dependent on initial and final position The force of gravity is a conservative force.

Examples for non-conservative forces
Initial position Final position Initial position Final position Friction force Applied force of pushing or pulling Initial position Final position Initial position Final position

Which of the following are conservative forces? Justify answer.
Friction Gravity close to the surface of the earth Force of the engine of a snow mobile Force exerted by a horizontal spring on a mass Drag force on a parachute at terminal velocity Gravity far away Normal force

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