**Work and Energy Worksheet-4**

- A car weighing 1000 kg and traveling at 30 m/s stops at a distance of 50 m decelerating uniformly. What is the force exerted on it by the brakes? What is the work done by the brakes?

- How much work is done when a body of mass m is raised to a height h above the ground?

- State the SI unit of work.

- Is work a scalar or a vector quantity?

- Define 1 joule of work.

- What is the condition for a force to do work on a body?

- Is energy a vector quantity?

- What are the units of (a) work, and (b) energy?

- What is the work done against gravity when a body is moved horizontally along a frictionless surface?

- By how much will the kinetic energy of a body increase if its speed is doubled?

**Answer:**

- In order to calculate the force, we have to find out the acceleration or retardation.

Initial speed, u = 30 m/s

Final speed, v = 0 (Since the car stops)

Acceleration *a *= ?

Distance s = 50 m

Now, we know that:

v^{2} = *u ^{2} + 2as*

So, (0)^{2} = (30)^{2} + 2 × a × 50

100 *a = –*900

a =–(900/100)

Acceleration, *a* =* –*9 m/s^{2 }

The force exerted by the brakes can now be calculated by using the formula :

* F *=* m *×* a*

Here, Mass, *m *= 1000 kg (Given)

Acceleration, *a* = –9 m/s^{2}

Force, F = 1000 × (–9)

F = –9000 N

Thus, the force exerted by the brakes on the car is of 9000 newtons. The negative sign shows that it is a retarding force.

The work done by the brakes :

* W* = *F* × *s*

Here, Force, F = 9000 N

Distance, s = 50 m

So, Work done, W = 9000 × 50 J

= 450000 J

= 4.5 × 10^{5} J

Thus, the work done by the brakes is 4.5 × 10^{5} joules.

- m × g × h

- Joule

- vector

- When a force of 1 Newton moves a body through a distance of 1 meter in its own direction, then the work done is known as 1 joule. This is

1 joule = 1 Newton ´ 1 meter

Or 1 J = 1 Nm

- The force should produce motion in the body.

- No it is a scalar quantity

- Joule

- Zero

- Becomes four times