Mechanics: Forces in Equilibrium

Question 1

What does it mean for an object to be in equilibrium?

Answer 1

Object is at rest or moving at a constant velocity. Requires for the resultant force to be zero, and for the moments of the forces to be balanced i.e. no turning effect.

Question 2

3 forces rule on point in eqm?

Answer 2

Resultant force is zero only if the resultant on any two of the forces is equal and opposite to the third force.
F1 + F2 = - F3
Vector sum of F1 + F2 + F3 = 0

Question 3

Block on a rough slope eqs for F, S, W, θ.

(F = friction
W = weight
S = support force)

Answer 3

F = W sinθ
S = W cosθ
W^2 = F^2 + S^2
tanθ = F/S

θ = angle between weight force and support force when extended, and also between slope and horizontal.

Question 4

Imagine string holding weight, attached to two other strings at a middle point. Each of the other two strings go north west/east around pulleys, holding up the middle string and their own weights also. Consider each weight to be equal to the tension in that string. θ1 is between centre string and NW string, θ2 is between centre string and NE string. Prove 3 force rule for system in eqm.

Answer 4

Use parallelogram rule. Draw to scale the three forces exactly as they are around the central point. Draw two dotted lines each parallel to NE or NW line. They join and make a parallelogram. Draw a final dotted line from the central point to where the two dotted lines meet. This is value of F3. If F1 + F2 = F3, then true.

Question 5

What is moment?

What are the units?

Answer 5

The moment of a force about any point = the force x the perpendicular distance from the line of action of the force to the point.
Moment = F x d (Nm)

Question 6

What is a body?

Answer 6

An object that is not a point object.

Question 7

What is the principle of moments?

Answer 7

For a system in eqm, the sum of the clockwise moments = sum of the anticlockwise moments.

Turning effects of forces balanced.

Question 8

When there are multiple unknown forces, how to choose pivot and why?

Answer 8

Take moments about a point through which one of the unknown forces acts. This point, the pivot, will give the force acting through it a moment of zero because d = 0.

Question 9

What is the centre of mass of a body?

Answer 9

The point through which a single force on the body has no turning effect.

The point through which ALL the weight of the body acts.

Question 10

Describe relationship between d and turning effect for a spanner turning a nut?

Answer 10

In moments, increasing d increases turning effect of force. But if spanner is too long and the nut too tight, the spanner could snap if too much force is applied.

Question 11

For a system in equilibrium, state two conditions.

Answer 11

No resultant force.
No resultant moment.

Question 12

Single-support problems: support force and moments.

Imagine uniform plank with weight W0 and support force acting at W0 position. Think up eqs.

Answer 12

When object in eqm is supported at one point only, support force is equal and opposite to total downward force.
S = W1 + W0 + W2
W1d1 = W2d2 because no turning effect.

Question 13

Two-support problems: support force and moments/

Imagine now a beam supported 1/4 of the way by S1 and at the furthest end by S2, with weight W. Think up eqs.

Answer 13

Sum of support forces is equal and opposite to total downward force.
S1 + S2 = W
Value of S1 larger than S2 because d1 is smaller and no turning effect.

Question 14

What is a couple?

Answer 14

A couple is a pair of equal and opposite forces acting on a body, but not along the same line.

Question 15

What is the moment of a couple?

Answer 15

Force x perpendicular distance between the lines of action of the forces. Total moment = F x d.
Total moment is the same regardless of pivot point chosen.

(so d is distance between the couples, and F is the force of one of them bc its the same value anyways)

Question 16

What happens when a body in stable eqm is displaced and released?

Answer 16

It returns to its eqm position.

Question 17

Why does it return to its eqm position?

Answer 17

Centre of mass of object directly below point of support when at rest, therefore W equal and opposite to S when in eqm. When displaced, the weight no longer passes through the point of support so weight returns the object to eqm.

Think of moments here. Weight has turning effect when displaced bc not acting through pivot point/support force point.

Question 18

What happens when a body in unstable eqm is displaced?

Eg plank balanced on drum.

Answer 18

Will not return to eqm. Plank will roll off drum.

Question 19

Why does this happen?

Answer 19

Centre of mass of plank is directly above the point of support when in eqm. S = - W
if plank displaced, centre of mass no longer above point of support, therefore weight acts to turn plank further from eqm position.

Weight force has turning effect that moves it further from eqm rather than closer as before.

Question 20

Why are bowling skittles easy to knock over.

Answer 20

They’re tall so their centre of mass is high, and the base is narrow. Therefore small nudge causes tilt then topple.

Question 21

Imagine a bookcase of length l and width b. Force applied from the left at a height some point along l (not full length l). Bookcase in contact with floor on right side at point P (pivot point while it tilts).

Answer 21

Ok.

Question 22

What is meant by tilting?

Answer 22

This is when an object at rest on a surface is acted on by a force that raises it up on one side.

Question 23

Apply tilting to the bookcase described above.

Think about the cw and acw moments, and the pivot point.

Answer 23

To make bookcase tilt, the force must turn it clockwise at point P. The entire support from the floor acts at point P. The weight of the bookcase provides an anticlockwise moment about P.

Cw = F x d, where d is perpendicular distance from line of action of F to pivot (so from floor to where F force line acts).
Acw = Wb/2.

Therefore for tilting to occur
Fd > Wb/2

Question 24

What is meant by toppling? What’s the condition for toppling?

Answer 24

If an object on a flat surface is tilted more and more, the line of action of the weight passes closer and closer to the pivot. If the object is tilted so much that the line of action of its weight passes beyond the pivot, the object will topple over if allowed.

Question 25

What’s the furthest the object can be tilted without toppling?

Eg car on slope?

Answer 25

The position where the line of action of the weight passes through the pivot.

If slope too great, line of action of weight passes beyond wheelbase so topples over.

Question 26

What’s a free body diagram?

Eg parked car on a slope forces?

Answer 26

Diagram that shows only the forces acting on the object (doesn’t inc the equal and opposite forces present).

Eg force of friction, support forces up at wheels, weight down.

Question 27

3 force rule for a body in eqm?

Answer 27

Valid as long as their lines of action intersect at the same point, otherwise the body can’t be in eqm as the forces will have a net turning effect.

For the car eg above, weight down from centre of car, friction along base of car parallel to slope, support force acts from where the two other forces intersect in perpendicular direction to slope.

Question 28

Scale diagram of forces to solve for unknown force. Eq?

(θ1 is the angle opposite F1 in triangle etc)

Answer 28

Make a triangle by connecting all at correct angles, and doing dotted line for unknown.
F2 sinθ3 = F3 sinθ2

So F1/sinθ1 = F2/sinθ2 = F3/sinθ3