Topic 5 Forces, density and pressure; chapter 4

Question 1

what is the purpose of a sign convention?

Answer 1

if used correctly , the sign of your answer will tell you the direction of the resultant force.

Question 2

what are some points to note when drawing a scale drawing?

Answer 2

1- state the scale used

2- draw a large diagram to reduce uncertainty

Question 3

what happens when downward force = horizontal force ?

Answer 3

the angle of the resultant force is 45 degrees.

Question 4

what does a closed diagram represents?

Answer 4

set of vectors drawn using the vector diagram that has the resultant force of zero form a closed diagram.
Therefore, a closed diagram such as a closed triangle represents that the object is in equilibrium.

Question 5

what can we deduce when we know that the forces on an object are equilibrium?

Answer 5

the forces must add up to zero. therefore, we can find the values of one or more unknown forces.

Question 6

what is a feature of perpendicular components of a vector?

Answer 6

perpendicular components of a vector are independent of one another. that is, a change in one will have no effect on the other.

Question 7

what is meant by resolving vectors?

Answer 7

splitting up a vector into horizontal and vertical components is known as resolving vectors. the components are in two directions at right angles to each other.

Question 8

what is the cosine of 90?

Answer 8

zero

Question 9

what is the sine of 90 ?

Answer 9

one

Question 10

what is the relationship between cos(90-@) and sin(@) ?

Answer 10

cos(90-@) = sin(@)

Question 11

what is the formula of newton’s second law for constant mass ?

Answer 11

a = f/m

Question 12

what is the relationship between force, acceleration and weight ?
OR
how can we find the resultant force acting on an object using horizontal and vertical components of forces acting on the object?
OR
what is the formula of resultant force acting on an object that is moving on a slope?

Answer 12

f = mg sin(@) where f = resultant force; N
m = mass; kg
g= gravitational potential energy;
9.81 ms^-1 (mg = weight)
@= angle with the horizontal

Question 13

how can the weight be resolved?

Answer 13

weight(W)’s
vertical component= perpendicular to ground(or slope)
horizontal component= parallel to the ground(or slope)

Question 14

what is the formula of acceleration when f= mg sin(@) and a= f/m `? OR
what is the formula of acceleration of an object moving on a slope?

Answer 14

f = mg sin (@) 
a = f/m 

a= mg sin(@) / m
therefore,
a = g sin(@)

Question 15

what is the relationship between acceleration and the steepness of slope?

Answer 15

the steeper the slope (the greater the value of sin(@)) and hence the greater the trolley’s acceleration.

Question 16

is it easier to move a box if the rope is horizontal or if the rope is sloping upwards?

Answer 16

it is easier to move the box when the rope is horizontal. this is because the force pulling the box is the horizontal component of F.
the horizontal component of F is Fx

Fx= Fcos(@) where @ is the angle between F and Fx.

when the rope is horizontal, @ = 0.
therefore Fx= Fcos(0)
= F

when the rope is sloping upwards, @ is not equal to 0.
therfore, Fx=Fcos(@) .

F is bigger than Fcos(@).
therefore horizontal component of F is bigger when the rope is horizontal.

Therefore, it is easier to pull the box when the rope is horizontal.

Question 17

what is the centre of gravity?

Answer 17

the point where all the weight of the object may be considered to act.

Question 18

how can the centre of gravity of a thin sheet, or lamina, of cardboard or metal be found?

Answer 18

centre of gravity can be found by suspending the sheet freely from two or three points.

a length of the string is attached to the pin. the other end of the string has a heavy mass attached to it. this is called the plumb line.

a line is drawn along the vertical string of the plumb line of different points.

the point where these lines intersect is the centre of gravity.

Question 19

what is a moment?

Answer 19

a quantity which tells us the turning effect of a force is its moment.

Question 20

what is the formula for moment of a force?

Answer 20

moment of a force = force * perpendicular distance from the pivot.

Question 21

what is the unit of moment?

Answer 21

newton metre Nm

Question 22

what happens when the force applied is at an angle to the lever(pivot), rather than at 90 degrees?

Answer 22

when the force applied is not perpendicular to the pivot, it has a lower turning effect.

Question 23

what is the moment of a force which is applied at an angle to the pivot? (angle which is not equal to 90 degrees)

Answer 23

moment of a force = F*x where F = force N
x = distance between pivot and force from the point where force is perpendicular to the pivot.

x= d*sin(@) —refer to fig 4.17 on page no. 60.

therefore,
moment of force = F* d*sin(@) where f= force N
d= perpendicular
distance from the pivot
@= angle between the
line of action of the force and the
lever(perpendicular distance)

Question 24

what is the turning effect of a force passing through the pivot?

Answer 24

zero
moment of force = F*perpendicular distance

perpendicular distance = 0 when force is passing through pivot.

therefore, moment= 0

Question 25

what is the principle of moments ?

Answer 25

for any object that is in equilibrium,
sum of clockwise moments = sum of anticlockwise
about any point moments about the same
point

Question 26

what is a characteristic of an object in equilibrium ?

Answer 26

no resultant force acts on the object

Question 27

what is a couple?

Answer 27

a couple is 2 forces equal in magnitude but opposite in direction that create a turning effect but doesn’t cause the object to accelerate

Question 28

what is a torque?

Answer 28

the turning effect or the moment of an a couple is known as a torque.

Question 29

what are the requirements to form a couple?

Answer 29

to form a couple, the two forces must be:

• equal in magnitude
• opposite in direction, parallel
• separated by a distance, d

Question 30

how can the torque of a couple be calculated?

Answer 30

torque of a couple can be calculated by adding the moments of each force.
OR
torque of a couple = one of the forces * perpendicular
distance between
the forces

Question 31

what is the relationship between the distance between force and pivot and the moment of the force?

Answer 31

the further the force is from the pivot, the greater the moment.

Question 32

what is the difference between the moment of a force and the torque of a couple?

Answer 32

the torque of a couple doesn’t depend on the point about which it acts, only on the perpendicular distance between the two forces.

Question 33

what is the difference between a single force acting on an object and a couple acting on an object?

Answer 33

even though both types of forces doesn’t require a pivot;
when a single force acts on an object, the object will accelerate
but
a couple is a pair forces equal in magnitude and opposite in direction, so it will not make the object accelerate.

Question 34

what are the 2 conditions to be fulfilled for an object to be in equilibrium?

Answer 34

• the resultant force acting on the object must be zero

- the resultant moment is zero