# Questions for Forces and Dynamics (JC) Set 2

An object of mass 1.5 kg is sliding with a velocity of 3.0 m s-1 on a frictionless surface towards another object which is stationary and has a mass of 2.0 kg. This head-on collision is completely inelastic. If the duration of the collison is 0.050 s, find the average force that is exerted between the objects during the collision.

1. 39 N
2. 51 N
3. 90 N
4. 119 N

By COM,
m1u1 + m2u2 = (m1 + m2)v
(1.5)(3.0) = (1.5 + 2.0)v
v = 1.29 m s-1
By Newton 2nd‘s Law, < F >Δt = Δp

Consider 1.5 kg mass:
< F >(0.050) = (1.5)(1.29 – 3.0)
< F > = -51.3 N

Consider 2.0 kg mass:
< F >(0.050) = (2.0)(1.29 – 0)
< F > = 51.6 N

A particle which moves from rest is acted upon by two forces: a constant forward force and a retarding force which is directly proportional to its velocity. Which one of the following statements about the subsequent motion of the particle is true?

1. Its velocity increases from zero to a maximum.
2. Its acceleration increases from zero to a maximum.
3. Its velocity increases from zero to a maximum and then decreases.
4. Its acceleration increases from zero to a maximum and then decreases.
The net force on the particle decreases as the velocity increases. When the retarding force is equal to the constant forward force, the net force becomes zero. The velocity of the particle is at the maximum.

An aircraft in level flight is moving with a constant velocity relative to the ground. The resultant force acting on the aircraft is equal to:

1. the weight of the aircraft
2. the resultant of the air resistance and the thrust of the engine
3. the resultant of the air resistance and the weight of the aircraft
4. zero
An object traveling at constant velocity implies that it has zero acceleration. Therefore, the resultant force acting on it is zero.

A steady stream of balls, each of mass 0.40 kg and speed 15 ms-1, hits a vertical wall at right angles. After hitting the wall, the balls rebound with the same speed.

Given that 600 balls hit the wall every 10 seconds, calculate the average force acting on the wall. (You may assume that the incident and rebounded balls do not collide.)

1. 0 N
2. 120 N
3. 360 N
4. 720 N

\begin{aligned} \left< F \right> &= N \frac{d \left( mv \right)}{dt} \\ &= \frac{600 \left( 0.40 \right) \left(-15-15 \right)}{10} \\ &=-720 \, \text{N} \end{aligned}

is the average force acting on the balls by the wall. By Newton’s 3rd law, the average force acting on the wall is 720N.

A ball falls vertically and bounces on the ground.

The following statements are about the forces acting on the ball while it is in contact with the ground. Which statement is correct?

1. The force that the ball exerts on the ground is always equal to the weight of the ball.
2. The force that the ball exerts on the ground is always equal in magnitude and opposite in direction to the force that the ground exerts on the ball.
3. The force that the ball exerts on the ground is always less than the weight of the ball.
4. The weight of the ball is always equal in magnitude and opposite in direction to the force that the ground exerts on the ball.

By Newton’s 3rd law, the two interacting forces will act on different bodies but not on the same body.