Equilibrium and momentum

Question 1

What is rotational motion? What force causes this?

Answer 1

Motion of an object about an axis causes by perpendicular forces to that axis.

The effective force causing rotation around an axis is called torque (L)

Question 2

Give the formula for torque and explain it.

Answer 2

L (torque) = (force)(distance from pivot point)

Think of pushing a door. Pushing near hinge is hard, but pushing near edge of door is easy. Multiply distance from hinge by force used to get the amount of torque applied.

Question 3

If there are multiple torques acting on a rotating object, how do you find out the direction of motion?

When is an object at equilibrium?

Answer 3

Find the net torque. Assign a direction an arbitrary positive or negative and sum the torques together.

An object is at equilibrium when the net forces and the net torques acting upon the object is zero. (the object is motionless or moving at a constant velocity, due to its internal inertia)

Question 4

What are the measure of inertia for

1. translational motion
2. rotational motion

Answer 4

Translation: mass

Rotational: moment of inertia (l = Σmr^2)
- Where r is distance from axis of rotation

Question 5

What is momentum? What is linear momentum?

Answer 5

• A vector quantity
• Product of mass and velocity of an object

M = mv

Linear momentum is a measure of the tendency of an object to maintain motion in a straight line. The greater the momentum (M), the greater the tendency of the object to remain moving along a straight line in the same direction. The momentum (M) is also a measure of the force needed to stop or change the direction of the object.

Question 6

What is a measure of the force needed to stop or change the direction of motion of an object?

Answer 6

Momentum (M = mv)

Question 7

What is the ‘impulse’ (I) of an object? (give the formula to calculate it)

Answer 7

The measure of the change of the momentum of an object. It is the product of the force applied by the time during which the force was applied to change the momentum.

I = F(Δt) = ΔM

M = momentum = (mass)(velocity)
F = acting force
Δt = Time elapsed during force applied

Question 8

True or false? Momentum is conserved (like energy)

Answer 8

True!

The total linear momentum of a system is constant when the resultant external force acting on the system is zero.

Question 9

Consider a simplified model of continent collision, where the continents are circular, uniform slabs of identical thickness and free to move on a frictionless fluid mantle surface.

When continents collide, what is conserved?

Answer 9

Momentum

The collisions of continents is an inelastic event. The collision caused deformation that resulted in mountain building. Only momentum is conserved in an inelastic collision (eg. kinetic, potential and impulse energy are not conserved)

Question 10

A continent of mass m collides with a continent of mass m/2 that is initially at rest. During the collision, the more massive continent is found to exert a force F on the less massive continent, causing the smaller continent to accelerate. At the same time, the less massive continent exerts a force on the larger continent of magnitude ___?

Answer 10

F

Newton’s third law (an action force is equal and opposite to the reaction force) requires that the mutual forces exerted during continent collisions be equal in magnitude.

Question 11

Which of the following is equal to a change in momentum of an object?

A. Force
B. Acceleration
C. Impulse
D. Velocity

Answer 11

C. Impulse

A change in momentum can be accomplished by the action of a force F over a time interval Δt. This product (FΔt) is referred to as an impulse.

Question 12

What is strain and how is it calculated?

Answer 12

Strain is the ratio of stretching, it is a measure of how much something is willing to bend with a given force. It can be calculated by:

ΔL/L

Where L = length

Question 13

What is stress and how is it calculated? Give relationship and Young’s modulus to show the practical application of stress and strain together.

Answer 13

Stress is similar to pressure, in that it depends on surface area to predict how a force will influence the ‘strain’ on an object.

Stress = F/A

Relationship: F/A = Y(ΔL/L)
AKA: Stress = (Y)(Strain)
Y = Young’s modulus (N/m^2)

Question 14

Write the formula for the relationship between stress and strain with when shear forces are applied to an object

Answer 14

F/A = S(Δx/L)

S is the shear modulus (N/m^2)

Question 15

Is it easier to stretch a rod or compress it? Why?

Answer 15

Neither. The shortening ΔL due to a compressive force (pushing) is the same as the lengthening ΔL due to an equal sized tensile force.

F = (A)(Y)(ΔL/L)

A: area
L: length
Y: Young’s modulus (N/m^2), depends only on material

Question 16

When do the shear and stress/strain formulas become effective? What is the elastic limit?

Answer 16

These relationships become effective when the material becomes elastic.

When a force is applied to something to produce stress (causing strain or shearing), the point at which the constituent particles of the material begin to flow and cause the material to go soft is the elastic limit.

Question 17

Why is it more painful to land on a sidewalk than to land on a trampoline?

Answer 17

You have a greater impact time with the trampoline, which causes a smaller magnitude of force on you. This makes sense when given the formula for an impulse (the change in momentum)

I = FΔt

Which can be rewritten as:

F = I/Δt (longer impact time = smaller force)