Newton's First Law of Motion

Question 1 

Newton’s first law states that “a body in a state of rest or in motion at a constant velocity in a straight line will remain in the state of rest or in motion at a constant velocity in a straight line unless it is acted upon by a net external force.” 

Newton’s second law states that “the acceleration of an object is directly proportional to the net force acting upon the object and inversely related to the mass of the object.” 

Newton’s third law states that “the exertion of a force by one object say, X, onto another object, say Y, is met with the exertion of a force of equal magnitude but opposite in direction back onto object X by object Y”. The law is simplified as, “for every action, there is an equal but opposite reaction.” 

Question 2 

Force is a vector quantity because it defined by both its magnitude and direction. Besides its magnitude, the direction in which a force is crucial in describing a force. Quantities possessing both magnitude and direction are referred as vector quantities, thus force is a vector quantity. 

Question 3 

The net force is the summation of all the four forces 

F net = F 1 + F 2 + F 3 + F 4 

Question 4 

Mass is the amount of matter in a substance while weight is the force acting on an object due to the effect of gravity. The mass of an object remains constant and does not vary with changes in gravitational force. On the other hand, the weight of an object varies due to the effects of gravity in different places. The weight of an object may even be zero if the acceleration due to gravity in a particular location is zero. 

Question 5 

Force = mass × acceleration 

F = ma 

Where m is the mass and a = the acceleration due to gravity (9.80 m/s² or 9.8 N/kg) 

Weight = force = 450 N 

Mass = Force / Acceleration = 450 N/ 9.8 N/kg = 45.92 kg (2 decimal places) (Answer) 

1 Newton = 0.224809 pounds 

Thus 450 N = (450N × 0.224809 pounds) / 1 N = 101.164 ≈ 101.16 pounds (2 decimal places) (Answer) 

Question 6 

Since the 3.0 and 4.0 N forces are acting at right angles, the resultant vector is determined using the Pythagorean theorem as: 

F net = √3² + 4² = √25 = 5.0 N 

According to Newton’s second law of motion: 

F = ma 

Where F is the force, m = mass and a = the acceleration 

a = F/m 

a = 5.0 N /2.0 kg = 2.5 N/kg = 2.5 m/s² 

Question 7 

Momentum = mass × velocity 

Mass = 12kg 

Velocity = 3 m/s 

Momentum = 12 kg × 3m/s = 36 kg . m/s 

Question 8 

Impulse is the product of the force acting on an object and the time interval over which the force acts. The impulse acting on an object is equated to the change in momentum of the object. 

Given: 

Mass of carton = 65 kg 

Initial velocity = 5 m/s 

Final Velocity = 0 m/s (brought to a stop) 

Change in momentum = m . final velocity – m . initial velocity 

Impulse = change in momentum 

Impulse = 65kg (0 – 5) m/s = - 325 kg . m/s 

1kg . m/s = 1 Ns 

Impulse required = 325 Ns 

Question 9 

Work done = Force × Distance 

Force = 12 N 

Distance = 1.8 m 

Work = 12 N × 1.8 m = 21.6 N . m 

1 N . m = 1 joule 

Work done = 21.6 joules 

Question 10 

Power = Work (J) / Time (s) 

Work = potential energy = 150 J 

Time = 3 s 

Power = 150 J / 3 s = 50 J/s 

1 J/s = 1 watt 

Power required = 50 W 

Question 11 

Kinetic energy (KE) = ½ mv² 

Mass = 2 kg 

Velocity = 4.0 m/s 

KE= ½ × 2 kg × (4.0 m/s) ² = 16 kg . m²/s² 

1 kg . m²/s² = 1 joule 

KE = 16 joules 

Question 12 

Gravitational energy = mass × gravitational force × height 

PE g = mgh 

Take the gravitational force, g = 9.80 m/s² 

Mass = 5kg 

h = 16 m 

Gravitational energy = 5 kg × 9.80 m/s² × 16 m = 784 kg . m²/s² 

Gravitational energy = 784 joules