1. Differentiate between kinetic energy and potential  energy.

- Kinetic energy is energy due to motion.

- Potential energy is energy due to position.

- An object raised uphill has potential energy.

- The work done to raise the object is equal to the increase of potential energy of the object.

2. What is principle of conservation of energy?

Principle of conservation of energy states that energy can neither be created or destroyed. It can only be converted from one form to another. For example a weightlifter changes energy from his muscles [chemical energy ] to potential energy of the weight when the weight is lifted. If the weight lifter releases the weight, the potential energy is converted to kinetic energy as the weight falls.

3. A railway engine of mass 20,000 kg moving at 3 m/s collides with and couples to an initially stationary train of wagons of total mass 10000 Kg. Calculate the speed of the engine and wagons just  after impact. To calculate the speed v just after impact, use the principle of conservation of momentum which is true for any type of collision.

Total initial momentum = 20000 × 3 = 60000 kgms^-1

Total final momentum = Total mass × v = 30000 v

Since the total final momentum = the total initial momentum

30000 v= 60000

Velocity(v) = 2 ms^-1

4. A parachutist of weight 700 N falls at a constant velocity. What is the upward force on the parachutist?

The parachutist is falling at a constant velocity. So the acceleration is zero, that is the net force (ma) is zero, which implies the upward force is equal to the downward force.

We know downward force = 700 N

So upward force should be equal and opposite to downward force which is equal to 700N

5. A car of mass 500kg is travelling along a horizontal road. The engine of the car is working at a constant rate of 5kW.  What is the acceleration of the car when its speed is 5m/s?

The engine of the car is working at a constant rate of 5kW

Velocity = 5 m/s

Power  = Force × velocity

Force = Power / Velocity = 5000/5 = 1000 N.

Force = mass x acceleration

Mass = 500 kg

Acceleration = Force / Mass  = 1000/500 =2  m/s²

6. A mass  of 50 kg is accelerated by a constant force 5N from rest to a speed of 2 m/s in 5 seconds. Calculate the distance moved and work done.

Mass(m) = 50 Kg

Force (F)= 5 N

Initial velocity (u) = 0 m/s

Final velocity (v) = 2 m/s

Time interval (t) = 5 seconds

Acceleration(a) = (v –u)/t = 2/5 = 0.4 m/s²

Distance moved (s) = ut + 0.5at² = 0.5 × 0.4 × 25 = 5 meter

Work done = Force × Distance moved = 5 × 5 =25 Newton.

7. A mass of 50 Kg is moved to height of 5 meter. What is the gain in potential energy?

Mass(m) = 50 Kg

Height(h) = 5 m

Acceleration due to gravity (g) = 9.8 m/s²

Gain in potential energy = mgh =50 x 9.8 x 5 = 2450 Joules

8. A crane is used to lower a container of weight 8500 N slowly at a steady speed onto flat ground. What is the tension in the crane cable?

The crane is lowering at a constant velocity [Refer the diagram below]. So the acceleration is zero, which is the net force (ma) is zero, which implies the upward force is equal to the downward force.

We know downward force = 8500 N

So upward force should be equal and opposite to downward force which is equal to 8500N.

So the tension on the cable = 8500 N

9. A lift of weight 5500 N carries a person of mass 84 kg to the top floor of a building at steady speed. What is the tension in the lift cable during this time?

The lift with the person is moving with a constant velocity which means the acceleration is zero.

Total weight = weight of lift + weight of person

= 5500 + 84 x 9.8 = 6323.2 Newton.

The tension on the lift cable = Total  weight 

= 6323.2 Newton.

10. Calculate the force needed to accelerate a ball of mass 0.25 Kg from rest to a speed of 20 m/s in a time of 10 second. How far does the ball move in this time when the force is acting on it?

Acceleration (a) = (v – u)/t = (20 -0)/10 = 2 m/s²

Mass (m) = 0.25 Kg

Force needed to accelerate the ball = ma = 0.25 × 2 = 0.5 N

Distance the ball will move in 10 seconds

s = ut + ¹/₂ at² = 0 + ¹/² + 2 × 10² = 100 meter.