Work changes motion energy
Work and kinetic energy.
Speeding up, slowing down
A force speeds up a trolley. Another force slows it down. A third force acts, but the trolley keeps the same velocity.
What do you think the work done by each force does to the trolley's kinetic energy?
What this lesson covers
The idea
For an object of mass m, the work in changing its velocity from u to v is W = (1/2)m(v² – u²), its change in kinetic energy; positive work raises it, negative work lowers it, zero work leaves it unchanged.
Speeding up, slowing down
A force speeds up a trolley. Another force slows it down. A third force acts, but the trolley keeps the same velocity.
What do you think the work done by each force does to the trolley's kinetic energy?
- Raises it, lowers it, leaves it the same
- Raises it each time
- Leaves it the same each time
Change the velocity
The block has a mass of 2 kg (an example). Set its velocity before and after.
Work is the change in K
Speeding up from 2 to 4 m s⁻¹ needed positive work of 12 J. Slowing down from 4 to 2 m s⁻¹ was negative work of −12 J. Equal velocities meant zero work. The work done equals the change in kinetic energy.
The work done in changing the velocity of an object of mass m from u to v is W = (1/2) m (v² − u²), which is its change in kinetic energy. Positive work raises it, negative work lowers it, and zero work leaves it unchanged.
Notes
W = (1/2) m (v² − u²) is the change in kinetic energy: positive work raises it, negative work lowers it, zero work leaves it unchanged.
Check yourself
A force changes the velocity of a 2 kg object from 0 to 3 m s⁻¹. What work is done, in J? Use W = (1/2) m (v² − u²).
Answer: 9 J
W = (1/2) × 2 kg × (9 − 0) = 9 J.
A force changes the velocity of a 4 kg object from 2 to 5 m s⁻¹. What work is done, in J?
Answer: 42 J
W = (1/2) × 4 kg × (25 − 4) = 42 J.
A force changes the velocity of a 2 kg object from 5 to 3 m s⁻¹. What work is done, in J?
Answer: -16 J
W = (1/2) × 2 kg × (9 − 25) = −16 J.
No work is done by the force on a moving object, and its velocity does not change. Its kinetic energy…
- increases. Positive work raises the kinetic energy. Here the work is zero.
- remains constant — correct. Yes!
- becomes zero. The object keeps moving with the same velocity, so its kinetic energy stays the same.