# Momentum and force multiple choice

• lpettigrew
In summary, the conversation discusses the rearrangement of the equation for kinetic energy in terms of momentum and provides an example of calculating kinetic energy for two bodies with different momentums. It also explains the relationship between the centripetal force and an object moving in a circle, and defines the equation for force as the change in momentum over change in time. The correct answer for the force calculation is 400,000 N.
lpettigrew
Homework Statement
I found these questions and have attempted to solve them fully. Could anyone comment on my reasoning to substantiate my choices? I find I usually overlook details in mutiple choice questions and stumble to an answer. I was most uncertain about part i.

i. A body of mass 2 kg is travelling with twice the momentum of a body of mass 4 kg. What is the ratio of the kinetic energy of the first body to the kinetic energy of the second body?
A. 2:1
B. 1:2
C. 4:1
D. 8:1

ii. A body is moving in a circle at constant speed, and is being acted upon by several forces. Which of the following is true?
A. The resultant of all these forces balances the centripetal force.
B. The resultant of all these forces is the centripetal force making the body accelerate towards the centre.
C. The resultant of these forces balances the centrifugal force.
D.In addition to the forces acting there must be a centripetal force towards the centre.

iii. A rocket is ejecting 800 kg of hot gases every second and the gases are leaving at a speed of 500 m/s relative to the rocket. This causes a force on the rocket of:
A. 100 000 000 N
B. 1.6 N
C. 400 000 N
D. 50 000 000 N
Relevant Equations
KE=p^2/2m
F=p/t
i. Rearranging the equation for kinetic energy in terms of momentum;
1/2mv^2=(mv)^2/2m=p^2/2m
Inputting the values given KE=1^2/2*4kg = 1/8 J
Kinetic energy of a body with twice the momentum; KE=2^2/2*2kg =1 J

The ratio of the kinetic energy of the first body to the second body is therefore, 8:1, since 1J=8*1/8J. (option D)

ii. I believe that the resultant of all these forces is the centripetal force making the body accelerate towards the centre. (option B). For an object moving in a circle, this resultant force is the centripetal force that acts perpendicular to the direction of motion, towards the centre of the circle.

iii. Force=change in momentum/change in time
Force=(800*500)/1
Force = 400,000 N (option C)

All good.

## 1. What is the difference between momentum and force?

Momentum is a measure of an object's motion, while force is a measure of the push or pull on an object. Momentum is a vector quantity, meaning it has both magnitude and direction, while force is a scalar quantity, meaning it only has magnitude.

## 2. How is momentum calculated?

Momentum is calculated by multiplying an object's mass by its velocity. The formula for momentum is p = mv, where p is momentum, m is mass, and v is velocity.

## 3. What is the relationship between momentum and force?

According to Newton's Second Law of Motion, force is equal to the change in an object's momentum over time. This can be written as F = Δp/Δt, where F is force, Δp is the change in momentum, and Δt is the change in time.

## 4. How does momentum affect an object's motion?

The greater an object's momentum, the harder it is to stop or change its direction. This is because a larger momentum requires a larger force to change it. In other words, an object with a larger momentum will have more inertia and will be more resistant to changes in its motion.

## 5. Can momentum be conserved?

Yes, according to the Law of Conservation of Momentum, the total momentum of a closed system remains constant. This means that in a collision or interaction between objects, the total momentum before the interaction is equal to the total momentum after the interaction.

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