P5: Forces

What is the difference between a scalar and a vector quantity?

A scalar has magnitude only; a vector has both magnitude and an associated direction.

Give three examples of scalar quantities.

Distance, speed, mass (any three from: distance, speed, mass, energy, temperature, time).

Give three examples of vector quantities.

Force, velocity, displacement, acceleration, weight, momentum.

How is a vector quantity represented by an arrow?

The length of the arrow shows the magnitude; the direction of the arrow shows the direction of the vector.

What is a contact force? Give two examples.

A force between objects that are physically touching. Examples: friction, air resistance, tension, normal contact force.

What is a non-contact force? Give two examples.

A force between objects that are physically separated. Examples: gravitational force, electrostatic force, magnetic force.

Is force a scalar or a vector?

Force is a vector quantity.

State Newton's equation for weight.

W = m × g (weight in N = mass in kg × gravitational field strength in N/kg)

What is the gravitational field strength on Earth?

Approximately 10 N/kg (9.8 N/kg in more precise calculations).

What is weight?

The force acting on an object due to gravity.

What is the centre of mass?

The single point at which the weight of an object may be considered to act.

How is weight measured?

Using a calibrated spring balance (newtonmeter).

What is the relationship between weight and mass?

They are directly proportional (W ∝ m).

What is a resultant force?

A single force that has the same effect as all the individual forces acting on an object combined.

What does it mean to resolve a force into two components?

A single force can be split into two forces acting at right angles to each other that together have the same effect.

How can vector diagrams be used with forces?

Scale drawings of vectors can determine the resultant of two forces (magnitude and direction) or show equilibrium.

What is work done?

Work is done when a force causes an object to move through a distance in the direction of the force.

State the equation for work done.

W = F × s (work done in J = force in N × distance in m)

How many joules is one newton-metre?

1 J = 1 N·m

What energy transfer occurs when work is done against friction?

Kinetic energy is transferred to thermal energy (the temperature of the object rises).

State Hooke's Law.

The extension of a spring is directly proportional to the force applied, provided the limit of proportionality is not exceeded.

State the equation for Hooke's Law.

F = k × e (force in N = spring constant in N/m × extension in m)

What is the spring constant?

A measure of the stiffness of a spring; the force needed per unit extension (units: N/m).

What is the limit of proportionality?

The point beyond which the extension is no longer proportional to the force - the spring does not obey Hooke's Law.

What is the difference between elastic and inelastic deformation?

Elastic: the object returns to its original shape when the force is removed. Inelastic: the object is permanently deformed.

State the equation for elastic potential energy stored in a spring.

Ee = ½ × k × e² (elastic potential energy in J = 0.5 × spring constant in N/m × extension² in m²)

What energy is stored in a stretched spring (within the limit of proportionality)?

Elastic potential energy.

Why must more than one force be applied to change the shape of a stationary object?

A single force would cause the object to accelerate (move), not deform.

What does a linear force-extension graph indicate?

The object obeys Hooke's Law - extension is proportional to force.

What is a moment?

The turning effect of a force.

State the equation for the moment of a force.

M = F × d (moment in Nm = force in N × perpendicular distance from pivot to line of action of force in m)

State the principle of moments.

For a balanced object, total clockwise moment about a pivot = total anticlockwise moment about that pivot.

How does a lever transmit the rotational effects of forces?

A small force applied at a large distance from the pivot can balance a large force applied at a small distance.

How does a gear system transmit the rotational effects of forces?

A large gear turns more slowly but with greater force; a small gear turns faster with less force, transmitting rotational effects between components.

State the equation for pressure.

p = F / A (pressure in Pa = force normal to a surface in N ÷ area in m²)

What is a fluid?

Either a liquid or a gas.

In what direction does the pressure in a fluid act on a surface?

Normal (at right angles) to the surface.

State the equation for pressure due to a column of liquid.

p = h × ρ × g (pressure in Pa = height of column in m × density in kg/m³ × gravitational field strength in N/kg)

Why does pressure in a liquid increase with depth?

There is a greater height of liquid (and therefore greater weight of liquid) above the point, creating more pressure.

Why does a submerged object experience an upthrust?

Pressure is greater on the bottom surface than the top surface, creating a net upward resultant force.

What factors determine whether an object floats or sinks?

Whether the upthrust (equal to weight of fluid displaced) is greater than, equal to, or less than the object's weight.

Describe the Earth's atmosphere.

A thin layer of air surrounding the Earth that gets less dense with increasing altitude.

Why does atmospheric pressure decrease with altitude?

There are fewer air molecules (less weight of air) above a surface at greater height, so fewer collisions per unit area.

How do air molecules create atmospheric pressure?

Air molecules collide with surfaces, and the force from these collisions per unit area creates pressure.

What is the difference between distance and displacement?

Distance is a scalar - how far an object moves. Displacement is a vector - includes both the straight-line distance and direction from start to finish.

What is the difference between speed and velocity?

Speed is a scalar (magnitude only); velocity is a vector (speed in a given direction).

Give typical speeds for walking, running and cycling.

Walking ≈ 1.5 m/s; running ≈ 3 m/s; cycling ≈ 6 m/s.

What is the typical speed of sound in air?

Approximately 330 m/s.

State the equation for speed.

s = v × t (distance in m = speed in m/s × time in s)

How do you calculate average speed for non-uniform motion?

Average speed = total distance ÷ total time.

What does the gradient of a distance-time graph represent?

Speed.

How do you find the speed of an accelerating object at a particular instant from a distance-time graph?

Draw a tangent to the curve at that point and calculate the gradient of the tangent.

What is acceleration?

The rate of change of velocity.

State the equation for acceleration.

a = Δv / t (acceleration in m/s² = change in velocity in m/s ÷ time in s)

What does a negative acceleration indicate?

The object is decelerating (slowing down).

What does the gradient of a velocity-time graph represent?

Acceleration.

What does the area under a velocity-time graph represent?

Distance travelled (displacement).

State the equation for uniform acceleration linking final velocity, initial velocity, acceleration and distance.

v² − u² = 2 × a × s

What is the approximate acceleration of free fall near the Earth's surface?

About 9.8 m/s² (or 10 m/s² as an approximation).

What happens to a falling object's acceleration as it reaches terminal velocity?

Acceleration decreases to zero as drag increases until it equals the gravitational force; the object then moves at constant (terminal) velocity.

What is terminal velocity?

The constant velocity reached by a falling object when the resultant force on it is zero (drag = weight).

What does circular motion require in terms of velocity?

Speed is constant but velocity is constantly changing (direction changes), so there is a centripetal force/acceleration.

State Newton's First Law.

An object remains stationary or moves at a constant velocity unless a resultant force acts on it.

Give an example of Newton's First Law for a moving vehicle.

A car at steady speed - the driving force balances the resistive forces, so resultant force is zero and speed is constant.

What is inertia?

The tendency of an object to continue in its state of rest or uniform motion.

State Newton's Second Law.

The acceleration of an object is proportional to the resultant force and inversely proportional to its mass.

State the equation form of Newton's Second Law.

F = m × a (resultant force in N = mass in kg × acceleration in m/s²)

What is inertial mass?

A measure of how difficult it is to change the velocity of an object; defined as force ÷ acceleration.

State Newton's Third Law.

Whenever two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction.

Give an example of Newton's Third Law.

A book resting on a table: the book pushes down on the table (its weight), and the table pushes up on the book with an equal normal contact force.

What is stopping distance?

The total distance a vehicle travels from when the driver sees a hazard to when the vehicle stops. It equals thinking distance + braking distance.

What is thinking distance?

The distance a vehicle travels during the driver's reaction time.

What is braking distance?

The distance a vehicle travels after the brakes are applied until it stops.

What is a typical range for human reaction time?

0.2 s to 0.9 s.

Give three factors that increase reaction time.

Tiredness, alcohol, drugs, and distractions (any three).

Give two factors that increase braking distance.

Wet/icy roads, worn tyres, worn brakes, greater speed (any two).

Why does greater speed increase stopping distance significantly?

Both thinking distance (proportional to speed) and braking distance (increases with speed squared) increase.

What energy transfer occurs when brakes are applied?

The friction force between brakes and wheel converts kinetic energy into thermal energy, heating the brakes.

Why are large decelerations dangerous?

They require very large braking forces, can cause brakes to overheat and may lead to loss of control.

How is the braking force estimated for a given deceleration?

Using F = m × a, where the deceleration is calculated from the speed change over the braking distance.

Define momentum.

Momentum = mass × velocity (p = m × v), measured in kg m/s.

Is momentum a scalar or a vector?

Momentum is a vector quantity.

State the law of conservation of momentum.

In a closed system, the total momentum before an event equals the total momentum after the event.

Two trolleys collide: trolley A (2 kg) at 3 m/s hits stationary trolley B (1 kg). They move together. What is their velocity?

Total momentum before = 2 × 3 = 6 kg m/s. After: 6 = (2 + 1) × v → v = 2 m/s.

State the equation linking force and rate of change of momentum.

F = m × Δv / Δt (force = rate of change of momentum)

How do safety features like air bags and crumple zones reduce injury?

They increase the time over which momentum changes, reducing the force (F = mΔv/Δt - longer time means smaller force).

How does a cycle helmet protect a rider using the concept of momentum?

It increases the time of impact (deformation of the foam), reducing the force on the skull for the same change in momentum.