4 Forces

Question 1

State the four types of friction.

Answer 1

Static friction, Sliding/kinetic friction, Rolling friction, Viscous forces/fluid friction (between moving fluids)

Question 2

Explain why the force required to keep an object sliding is less than the force required to start moving it.

Answer 2

Refer to the friction-force graph on pg 3 of notes

Static, limiting, kinetic friction

Question 3

How does tension change along a taut string?

Answer 3

Tension remains the same throughout the string when it is taut.

Question 4

Define Hooke’s Law. State the equation for Hooke’s Law.

Answer 4

Hooke’s Law states that the extension of a body is proportional to the applied load if the limit of proportionality is not exceeded. Equation: F = kx where k is the force/spring constant which is a measure of the stiffness of the spring and its value can be obtained by calculating the gradient of the force-extension (f-x) graph.

Question 5

State the equation for the energy stored in a spring.

Answer 5

Energy stored in a spring = work done in stretching spring = area under the F-x graph = 1/2Fx = 1/2kx^2

Question 6

Define a fluid.

Answer 6

A fluid is any substance that can flow.

Question 7

Define density.

Answer 7

The density of a substance is its mass per unit volume.

Question 8

State the factors that affect density.

Answer 8

(i) Temperature

(ii) Pressure

Question 9

Define pressure. State whether it is a scalar or vector quantity. State the units of pressure.

Answer 9

Pressure is defined as the force per unit area, where the force is acting at right angles to the area. It is a scalar quantity. Units of Pressure can be Nm^-2 or Pa

Question 10

State the equation to calculate pressure and the pressure when taking into account atmospheric pressure.

Answer 10

Pressure = phg where p refers to the density of the fluid (written as roe), h refers to the vertical depth below the fluid surface and g refers to the acceleration of free fall

When taking into account atmospheric pressure, pressure = atmospheric pressure + phg

Question 11

What is the pressure of 1 atmosphere?

Answer 11

1 atm = 1.013*10^5 Pa

Question 12

Explain how pressure changes at different points in the fluid at rest at a given depth.

Answer 12

A fluid can exert pressure in any direction. At any point in a fluid at rest, the pressure is the same in all directions at a given depth given by P = phg.

Question 13

Define upthrust. States its origin and direction.

Answer 13

Upthrust is the vertical upward force exerted on a body by a fluid when it is fully or partially submerged in the fluid due to the difference in fluid pressure. It originates from the centre of buoyancy (centre of the immersed section of the body) and acts vertically upwards.

Question 14

State Archimedes Principle.

Answer 14

Archimedes Principle states that the upthrust on a body in a fluid is equal to the weight of the fluid displaced by the body.

Question 15

Describe the forces acting on a sinking object.

Answer 15

Forces that originate from the same point at the centre of the object:

Weight of object W = pVg (p refers to the density of the object and V refers to the object’s full volume)

Upthrust U: pVg (p refers to the density of the fluid the object is submerged in, V refers to the full volume of the object)

If the object is denser than the fluid, W > U, the object will experience a net downward force given by Fnet = W - U. Hence, the object accelerates downwards and sinks.

Question 16

Describe the forces acting on a floating object.

Answer 16

Both forces are of equal lengths as the object is in equilibrium.

Weight of object W = pVg (p refers to the density of the object and V refers to the object’s full volume) This force originates from the centre of gravity of the object.

Upthrust U: pVg (p refers to the density of the fluid the object is submerged in, V refers to the volume of the object beneath the fluid surface/ volume of fluid displaced by the object) This force originates from the centre of buoyancy.

Since the object is floating in equilibrium, Fnet = U - W = 0. Thus, U = W and the weight of the fluid displaced by the object equal to the weight of the object.

Question 17

State the principle of flotation. What does this imply?

Answer 17

The principle of flotation states that for an object in equilibrium, the upthrust is equal in magnitude and opposite in direction to the weight of the object. This implies that a floating object displaces its own weight of fluid in which it floats.

Question 18

Describe how to find the portion of a floating object that is submerged in the fluid.

Answer 18

U = W
pV(submerged)g = pV(full volume)g
V(submerged)/V(full volume) = p(density of object)/p(density of the fluid)

Question 19

What is a viscous force associated with?

Answer 19

It is associated with the resistance that the object experiences due to a fluid when moving relative to each other. (When a body moves in a fluid, it collides continuously with the molecules of the fluid and the body imparts momentum to the molecule, exerting a force on it. By N3L, the molecule exerts an equal and opposite force on the body which causes it body to slow down.)

Question 20

What factors affect viscous force?

Answer 20

(i) Shape of the body (streamlined body minimises area exposed, less viscous force)
(ii) Speed of the body (At low speeds, F is directly proportional to v. However, at high speeds, F is directly proportional to v^2)
(iii) Viscosity of the fluid (does not depend on density!!)

Question 21

State the conditions required for a body to be in equilibrium.

Answer 21

(i) Resultant force on the body is 0 (translational equilibrium)
(ii) Resultant moment on the body about any axis is 0 (rotational equilibrium)

Question 22

Explain how forces can be in translational equilibrium.

Answer 22

Method 1: If the resultant force is zero, the vector sum of the forces must be zero. The forces will form a vector diagram which can be a closed triangle or closed polygon in one direction.

Method 2: Resolve the forces into two perpendicular components and equate the sum of the components in each direction (x and y) to zero

Question 23

Define the principle of moments.

Answer 23

The principle of moments states that for a body in rotational equilibrium, the sum of clockwise moments about any axis must equal the sum of all the anti-clockwise moments about the same axis.

Question 24

Define the moment of a force.

Answer 24

The moment of a force about an axis is defined as the product of the force and the perpendicular distance of the line of action of the force from the axis.

Question 25

What is a couple?

Answer 25

A couple consists of a pair of equal and opposite forces whose lines of action do not coincide.

Question 26

Define a torque of a couple.

Answer 26

Torque of a couple is the product of the magnitude of one of the forces and the perpendicular distance between the forces. (Torque of a couple = Fd)

Question 27

Explain whether a body acted on by a couple is in equilibrium.

Answer 27

A body acted on by a couple has zero resultant force hence it is in translational equilibrium. However, the couple will produce a turning effect hence the body is not in rotational equilibrium. Overall, the body is not in equilibrium.

Question 28

State the requirements for the lines of action of 3 coplanar forces acting on a body in equilibrium.

Answer 28

The forces must either all be parallel or all meet at a point. In the case of parallel forces, the sum of the downward forces must equal the sum of the upward forces. This is because if the line of action of the third force does not meet at the same point, it will cause a moment about the point and the object cannot be in rotational equilibrium. (Note: Direction of the force must be such that it forms a closed loop with the other forces to ensure translational equilibrium)

Question 29

Define centre of gravity.

Answer 29

CG of a body is the point at which its whole weight (or the resultant of the distributed gravitational attraction) appears to act.