# 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:

– work done and change in the kinetic energy of an object undergoing accelerated rectilinear motion in one dimension 𝑊=𝐹𝑠=𝐹𝑠cos𝜃
– changes in gravitational potential energy of an object in a uniform field ∆U = mg∆h

### 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 step-by-step 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?