# Tag Archives: conservation of energy

## Bullet embedded in wooden block

At a training exercise, a policeman fires a pistol. A bullet of mass 10.0 g leaves the pistol horizontally at a speed of 500 ms^{-1}. The bullet strikes and gets embedded in a stationary piece of wood of mass 1.0 kg which was suspended. Immediately after impact, the wood with the embedded bullet moves at a horizontal speed of 5.0 ms^{-1} and swings upwards to a vertical height of h from its initial position before stopping momentarily.

a) What is the initial kinetic energy of the bullet when it leaves the pistol?

b)What is the final kinetic energy of the wood and embedded bullet immediately after impact?

c) By comparing (a) and (b), what is the loss in kinetic energy? Account for this loss.

d) Calculate the vertical height, h, stating any assumption made. Assume the gravitational field strength is 10 N kg^{-1}.

**Solutions:**

a) 1250 J

b) 12.6 J

c) 1240 J. The loss in kinetic energy is converted to heat and sound energy when the bullet strikes the wood and is embedded.

d) 1.25 m

## Ratio of KE and GPE at various positions

A ball in thrown vertically up. D is the highest point the ball reached. Find the ratio of KE at B to the PE at C.

**Solutions: 1 : 1**

**To solve such question, you have to apply ****conservation of energy**. In other words, **total energy **of ball at any positions (A, B, C and D) is the **same** (no air resistance etc). There is no way to find KE as no speed is given. So to find KE, you need to find it indirectly with the help of PE.

Understand the concept here as there can be many variations of question asked.

## Conservation of Energy – demo

This is a typical demo to illustrate conservation of energy. It will definitely be safe to remain stationary (if you release the ball from rest) as some of the energy of the ball will be converted to other forms like work done against air resistance. Hence, it will never reach the same height it is released, so will not never touch you.

Of course, if you give the ball a push, you are giving additional energy to the ball. That additional energy enable the ball to reach a greater height, hence most likely it will hit your face =)

## Work done – Man jumps from height 3 m, what is the force exerted by his legs?

A boy of mass 40 kg jumps from rest from a platform of height 3 m. He lands by bending his knees and stops his body in 0.5 s after landing. What is the force exerted by his legs?

**Solutions: 620 N**

To solve this question, you need to apply conservation of energy (COE) to find the kinetic energy (KE) that the boy possesses just before he reaches the ground.

After which, you can solve the question using (1) Conservation of energy or (2) Kinematics to solve.

Using COE to find the KE just before he reaches the ground.

**Method 1: Using Conservation of Energy (COE)**

**Method 2: Using Kinematics**

You must know these 2 methods and always think along this 2 directions when dealing with such questions.