Conservation of Energy Calculation Problems
This topic is part of the HSC Physics course under the section Forces, Acceleration and Energy.
HSC Physics Syllabus

apply the special case of conservation of mechanical energy to the quantitative analysis of motion involving:
Energy Conservation Problems
The following video walks through 5 common calculation problems on the law of conservation of energy and conservation of mechanical energy.
Watch the video for stepbystep solutions to the following questions
Example 1
Consider a ball is thrown vertically upward in a vacuum (no air resistance).
(a) Describe the changes in the ball’s kinetic energy, potential energy and mechanical energy.
(b) What speed is required to throw a ball vertically upwards to reach a maximum height of 50 m?
Example 2
A box slides down a hill that is 250 m tall with an initial velocity of 10 m/s to the right. Assuming no friction and air resistance, what is the final speed of the box when it reaches the bottom of the hill?
Example 3
An 800 kg car travels along a horizontal road with an initial speed of 20 m/s. The driver lets the car come to a complete stop without braking over a distance of 160 m. What is the coefficient of kinetic friction between the tyres of the car and the road?
Example 4
A trolley rolls down a frictionless track with an initial speed of 10 m/s at A, 20 m above the ground. It reaches its lowest point at B (ground) before travelling upwards to reach C. The speed of the trolley at C is 8 m/s.
(a) What is the speed of the trolley at B?
(b) What is the height of C above the ground?
Example 5
A 500 kg car moving to the right at 30 m/s collides with another 800 kg car moving to the left at 20 m/s. After the collision, the 500 kg car is moving to the left at 2 m/s while the 800 kg car comes to a complete stop.
How much heat and sound energy are produced during this collision?