Section 3.1: Work and Kinetic Energy
In this section, we explore the concepts of work and kinetic energy, fundamental to understanding how forces change the motion of objects.
\( W = F \cdot d \cdot \cos\theta \)
Where θ is the angle between the force and displacement.
\( KE = \frac{1}{2} m v^2 \)
\( W_{net} = \Delta KE = KE_f - KE_i \)
Example 1
A 10 kg box is pushed 5 m across a frictionless floor with a force of 20 N in the direction of motion. Find the work done on the box and its final kinetic energy if it started from rest.
Work: \( W = F \cdot d = 20 \cdot 5 = 100 \text{ J} \)
Final kinetic energy: \( KE_f = W = 100 \text{ J} \)
Velocity: \( v = \sqrt{2 KE / m} = \sqrt{2 \cdot 100 / 10} = 4.47 \text{ m/s} \)
Example 2
A car of mass 800 kg accelerates from 10 m/s to 20 m/s. Calculate the net work done on the car.
\( \Delta KE = \frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2 = 0.5 \cdot 800 \cdot (400 - 100) = 120,000 \text{ J} \)
Practice Problems
- A 5 kg box is pulled 10 m by a force of 30 N at 60° to horizontal. Calculate the work done.
- An object of mass 2 kg moves at 4 m/s. Calculate its kinetic energy.
- A 3 kg object accelerates from 2 m/s to 6 m/s. Find the net work done.
- A 10 kg mass is pushed 8 m by a 40 N force along a frictionless surface. Find the work and final KE.
- A sled of 20 kg slides down a 5 m slope. Find work done by gravity (ignore friction).
- An object with KE = 50 J speeds up to KE = 200 J. Find the work done on it.
- A 15 kg box moves under a horizontal force of 50 N for 3 m. Calculate work and final speed.
- A car of mass 1000 kg accelerates from 15 m/s to 25 m/s. Find net work done.
- A 2 kg object is pulled 5 m at 30° to horizontal with 10 N. Find work done.
- An object of 4 kg moving at 3 m/s slows to 0. Find work done by friction.