# StudySquare

This page covers the following topics:

1. Newton's first law

2. Newton's second law

3. Newton's third law

Newton's first law states that an object will remain at rest or continue moving at a constant velocity, unless it is acted upon by an external resultant force. When there is no resultant force acting on an object, the object is said to be in equilibrium.

Newton's second law states that the acceleration of an object is directly proportional to the force acting on it, in the direction of the force, and inversely proportional to the mass of the object. This means an object accelerates in the direction of the resultant force being exerted on it, the value of this acceleration depending on the mass of the object.

Newton's third law states that when object A exerts a force on object B, then object B exerts an opposite force on object A. This implies that all forces exist in pairs which are called Newton’s third law pairs. These two forces must act on different objects, opposite directions, be of the same type of force and act along the same line and for the same time.

# 1

A rocket of mass 4 × 10⁶ kg takes off vertically with a thrust of 6.2 × 10⁷ N. Calculate the initial acceleration of the rocket by using g = 9.8 m/s².

F = m × a

6.2 × 10⁷ N − 4 × 10⁶ × 9.8 = 4 × 10⁶ kg × acceleration

acceleration = 5.7 m/s²

5.7 m/s²

# 2

A ping-pong ball of mass 0.2 kg is released from the bottom of a tube filled with water. Given that it accelerates towards the top at 1.6 m/s² and that the upthrust is 62 N, find the drag acting on the ball.

resultant force = upthrust − drag − weight

ma = upthrust − drag − mg

0.2 kg × 1.6 m/s² = 62 N − 0.2 kg × 9.8 m/s² − drag

drag = 62 N − 1.96 N − 0.32 N = 59.7 N (3 s. f.)

59.7 N

# 3

Water is released out of a nozzle with a force of 2875 N from the back of a jet ski of mass 350 kg. Calculate the initial acceleration of the jet ski.

By Newton's third law, since the nozzle is exerting a backwards force on the water, the water exerts an equal and opposite force on the nozzle, and thus the jet ski, in the forward direction. An external resultant force is now acting on the jet ski, therefore by Newton's second law, it will accelerate in its direction.

F = m × a

2875 N = 350 kg × acceleration

acceleration = 2875 N ÷ 350 kg = 8.21 m/s²

8.21 m/s²

# 4

A toy boat is powered by a small electric fan. Explain, using Newton's laws, how the toy moves forward.

When the fan is turned on, the fan exerts a force on the air in the backwards direction. By Newton's third law, the air exerts a force on the fan in the opposite direction, ie. the forward direction. This creates a resultant force on the boat in the forward direction, and so by Newton's second law, the boat accelerates in the direction of this force, and so moves forward.

The fan exerts a force on the air and an equal and opposite force is exerted on the fan. This generates a resultant force on the boat.

# 5

A ladder of weight 200 N resting on rough ground is leaning against a smooth wall. The normal reaction exerted by the wall on the ladder is 170 N. Find the normal reaction and the frictional force exerted by the ground on the ladder.

Newton's first law states that an object will remain stationary unless it is acted upon by an external resultant force. Since the ladder is stationary, the forces acting on it must be balanced.

Resolving vertically: w = N, therefore the normal reaction exerted by the ground on the ladder is 200 N.

Resolving horizontally: R = F, therefore the frictional force exerted by the ground on the ladder is 170 N.

N = 200 N, F = 170 N

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