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MOTION AND FORCES EDEXCEL

  • A force is either a push or a pull that one object exerts on another object.

  • It can produce, slow down, speed up, stop motion, or change its direction.

0. Previous knowledge

Vectors and scalars

  • A vector has magnitude and direction.

  • A scalar has just magnitude.

  • E.g., speed is a scalar, and velocity is a vector.

Vector diagrams

  • In vector diagrams, vector quantities such as forces are represented by an arrow.

  • The length of the arrow is proportional to the size of the force.

  • The direction of the arrow shows the direction of the force.

  • Steps to draw a vector:

    • 1. Choose an appropriate scale

    • 2. Measure the required angle using a protractor from the baseline/second force.

    • 3. Draw an arrow of length proportional to the force using the scale taken.

Adding vectors

Parallel vectors

  • If they are in the same direction, they will be added.

  • If they are in opposite directions, the resultant will be in the direction of the greater force and its size will be the difference of the two vectors.

  • If they are equal and opposite, there will be no resultant.

Non-Parallel vectors

  • Tip-to-tail method: redraw one of the vectors, placing the tail of the vector at the tip of the second vector. Join the two corners to get the resultant.

  • Parallelogram method: complete the parallelogram, the diagonal of the parallelogram will be the resultant.

1. Movement and position

Speed

  • Speed is the distance travelled per unit of time.

  • It is a scalar.

    • e.g., 5 m/s.

  • It is always positive.

  • Speed(v)=distancetravelled(d)timetaken(t)Speed \: (v) = \frac{distance \: travelled \: (d)}{time \: taken \: (t)}

  • Since distance is measured in meters, and time is measured in seconds, speed's unit is metres per second (m/s) or kilometres per hour (km/h).

Distance-time graphs

  • Distance-time graphs provide a record of how far an object has moved as time has passed.

  • Distance travelled is plotted on the vertical axis, and time is plotted on the horizontal axis.

  • The line's slope, or gradient, tells us the object's speed.

    • The steeper the line, the greater the speed.

  • Acceleration is when an object speeds up, as shown in diagram C.

  • Other distance-time graphs are also shown in the picture below:

Velocity

  • Unit: m/s (metres per second) or km/h (kilometres per hour).

  • Velocity is speed in a given direction, so it is a vector.

    • e.g., 5 m/s east.

    • We not only know how fast something is going but also where it's going.

  • It can be negative or positive.

  • Velocity:(V)=displacement:(d)time:taken:(t)Velocity \\: (V) = \frac{displacement \\: (d)}{time \\: taken \\: (t)}

  • Displacement means distance travelled in a particular direction from a specified point.

Average speed and average velocity

  • Speed or velocity refers to a specific time/point of a journey.

  • When calculating average speed/velocity, we calculate the speed/velocity of the entire journey.

  • This journey may include the resting time in between and any acceleration or deceleration in the journey.

  • Averagespeed(v)=distancemoved(d)totaltimetaken(t)Average \: speed \: (v) = \frac{distance \: moved \: (d)}{total \: time \: taken \: (t)}

  • Averagevelocity(v)=totaldisplacement(d)totaltimetaken(t)Average \: velocity \: (v) = \frac{total \: displacement \: (d)}{total \: time \: taken \: (t)}

Acceleration

  • Acceleration=(finalvelocity(v)initialvelocity(u))/timetaken(t)Acceleration = (final velocity (v) - initial velocity (u) ) / time taken (t)

  • It is a vector.

  • Acceleration is the rate of increase in velocity with time.

  • It is measured in m/s2m/s^2 (meters per second squared).

  • Deceleration means slowing down.

    • A negative acceleration simply means deceleration.

  • (Finalspeed(vu))2=(initialspeed (vi))2+2acceleration(a)distancemoved(d){(Final \: speed \: (vu))}² = {(initial \: speed \ (vi))}² + 2 * acceleration (a) * distance \: moved \: (d)

Velocity-time graphs

  • The gradient in the picture below is straight, which tells us that the velocity is increasing steadily.

    • This means that the acceleration is uniform.

  • Averagevelocity(v)=initialvelocity(vi)+finalvelocity(vf)2Average \: velocity \: (v) = \frac{initial \: velocity \: (vi) + final \: velocity \: (vf)}{2}

  • The area under a velocity-time graph is equal to the distance travelled by the object in a particular time interval.

Circular motion

  • When an object is travelling in a circle at constant speed, the velocity is always changing as the direction is constantly changing.

  • The resultant force of a circular motion is towards the center of the circle.

2. Forces and Shape

  • The unit used to measure force is the Newton (n).

    • A force of one newton will make a mass of one kilogram accelerate at one metre per second squared.

  • A force is a vector quantity.

Common forces

  • Weight is the pull of the gravitational force on an object.

  • The normal force is a reaction force, the upward push on an object from the ground.

  • Friction is a force that opposes motion.

Balanced and unbalanced forces

  • The resultant force is the sum of all individual forces acting upon an object.

  • When the forces acting on something are balanced, the object does not change the way it is moving.

    • Unbalanced forces acting on an object cause it to change the way it is moving.

  • Inertial mass is a measure of how difficult it is to change the velocity of an object.

    • Inertialmass(m)=force(f)acceleration(a)Inertial \: mass \: (m) = \frac{force \: (f)}{acceleration \: (a)}

Friction

  • Friction is the force that opposes motion between two surfaces in contact.

    • It causes objects moving to slow down and stop.

  • The kinetic energy of the moving object is transferred to heat as work is done by the friction force.

  • Reducing friction means that machines work more efficiently

    • Increasing friction helps tyres grip the road better.

Changing shapes

  • Sometimes, a force can make an object change shape, either permanently or temporarily.

Springs and wires

  • Springs are coiled lengths of certain types of metal, which can be stretched or compressed by applying a force to them.

  • They obey Hooke’s law, which states that the extension is directly proportional to the force causing it.

    • Hooke’s law only applies until the limit of proportionality, after which the object does not obey the law, and the extension is imbalanced.

    • A straight line on a graph of extension shows the object is obeying Hooke’s law.

  • If a spring is stretched beyond its elastic limit, it will not return to its starting length.

  • The extension doubles if two springs are connected to each other directly.

  • The extension halves a load attached to two springs in parallel as the load is shared.

  • Force(f)=mass(m)acceleration(a)Force \: (f) = mass\:(m)*acceleration\:(a)

Elastic bands

  • Elastic bands are another example of changing objects.

    • They do not follow Hooke’s law.

3. Forces and movement

Force, mass, and acceleration

  • The acceleration of an object depends on the size of the unbalanced force and the mass of the object.

  • Acceleration is inversely proportional to mass.

  • Force(f)=mass(m)acceleration(a)Force \: (f) = mass\:(m)*acceleration\:(a)

Human Reaction Time

  • Human reaction time is the time taken between a stimulus being presented and the initiation of a response by an individual.

  • The average human reaction time is 0.25 seconds.

  • Factors Affecting Reaction Time:

    • Age and health of the individual.

    • State of alertness and concentration.

    • Influence of drugs or alcohol.

    • Nature of the stimulus (visual, auditory, etc.).

Stopping Distance

  • Stopping distance is the total distance covered by a vehicle from the moment the driver perceives a hazard until the vehicle comes to a complete stop.

  • Components of stopping distance:

    • Thinking Distance: The distance traveled by the vehicle during the driver's reaction time.​

    • Braking Distance: The distance traveled by the vehicle while the brakes are applied and the vehicle decelerates to a stop.

  • Factors affecting stopping distance:

    • Speed of the vehicle.

    • Road surface conditions (dry, wet, icy).

    • Condition of tires and brakes.

    • Reaction time of the driver.

Weight

  • The weight of an object is the force that acts on it because of gravity.

  • The gravitational field strength is the force that acts on each kilogram of mass.

  • Weight(w)=mass(m)gravity(g)Weight \: (w) = mass\:(m)*gravity\:(g)

  • Gravity on Earth is approximately 9.81N.

Air resistance and terminal velocity

  • Air resistance, or drag, is a frictional force that opposes motion in air. It slows down anything travelling through the air and may also cause the object to heat up.

  • The drag coefficient is a measure of how easily an object moves through the air.

  • Terminal velocity is when the drag force has increased to the point where it exactly balances the weight force.

  • Since there is now no unbalanced force on the object its acceleration is also zero.

Work

  • The work done to stop an object is equal to the initial kinetic energy of the object.

  • KE=Fd=12mu2KE=Fd=\frac{1}{2} mu²

4. Momentum

  • Momentum is a measure of how difficult it is to stop something that is moving.

  • Momentum(p)=mass(m)velocity(v)Momentum \: (p) = mass\:(m)*velocity\:(v)

  • It is a vector quantity, measured in kilogram metres per second (kg m/s).

Momentum and acceleration

  • The rate of change of momentum of an object is proportional to the force applied to the object.

  • Force(F)=finalmomentum(mf)initialmomentum(mi)timetaken(t)Force \: (F) = \frac{final \: momentum \: (mf) \: - \: initial \: momentum \: (mi)}{time \: taken \: (t)}

Momentum and collisions

  • The total momentum of objects that collide remains the same.

Newton’s Laws of Motion

Newton's first law

  • An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.

Newton's second law

  • When a resultant force acts on an object of a constant mass, the object will accelerate in the direction of the resultant force.

  • The product of the mass and acceleration of the object gives the resultant force.

  • Force(f)=mass(m)acceleration(a)Force \: (f) = mass\:(m)*acceleration\:(a)

Newton's third law

  • Every action has an equal and opposite reaction.

  • F1=F2F₁=F₂

    mass1acceleration1=mass2acceleration2mass_1 * acceleration_1 = mass_2 * acceleration_2

5. The turning effect of forces

The moment of a force

  • A moment is the turning effect of a force.

  • They occur when a force causes an object to rotate about a pivot or hinge.

  • The size of the moment is determined by the size of the force and the perpendicular distance from the pivot.

  • Moment(M)=force(f)perpendiculardistancefrompivot(d)Moment \: (M) = force \: (f) * perpendicular\:distance\:from\:pivot\:(d)

  • The unit of moments is Newton Metres (Nm).

  • Opening or closing a door is an example of a moment.

Principle of Moments

  • The Principle of Moments states that for an object to be balanced, the clockwise moment must be equal to the anticlockwise moment.

  • F1D1=F2D2F_1 * D_1 = F_2 * D_2

Centre of Mass and Stability

  • The centre of mass of an object is the point at which the weight of the object acts.

  • For symmetrical objects, the centre of mass is at the point of intersection of its symmetries.

  • When an object is suspended, its centre of mass will come below it.

  • To find the centre of mass of a lamina, it is suspended from a point and a plumb line is hung next to it.

    • A line is drawn using a pencil along the plumb line.

    • This is repeated from multiple points, the point of intersection of the lines is the centre of mass.

  • An object is stable when its centre of mass is above its base.

  • If the centre of mass is not directly above its base, the object will topple over.

  • The lower the centre of mass of an object, the greater the stability.

    • The greater the base area of an object, the greater the stability.

YS

MOTION AND FORCES EDEXCEL

  • A force is either a push or a pull that one object exerts on another object.

  • It can produce, slow down, speed up, stop motion, or change its direction.

0. Previous knowledge

Vectors and scalars

  • A vector has magnitude and direction.

  • A scalar has just magnitude.

  • E.g., speed is a scalar, and velocity is a vector.

Vector diagrams

  • In vector diagrams, vector quantities such as forces are represented by an arrow.

  • The length of the arrow is proportional to the size of the force.

  • The direction of the arrow shows the direction of the force.

  • Steps to draw a vector:

    • 1. Choose an appropriate scale

    • 2. Measure the required angle using a protractor from the baseline/second force.

    • 3. Draw an arrow of length proportional to the force using the scale taken.

Adding vectors

Parallel vectors

  • If they are in the same direction, they will be added.

  • If they are in opposite directions, the resultant will be in the direction of the greater force and its size will be the difference of the two vectors.

  • If they are equal and opposite, there will be no resultant.

Non-Parallel vectors

  • Tip-to-tail method: redraw one of the vectors, placing the tail of the vector at the tip of the second vector. Join the two corners to get the resultant.

  • Parallelogram method: complete the parallelogram, the diagonal of the parallelogram will be the resultant.

1. Movement and position

Speed

  • Speed is the distance travelled per unit of time.

  • It is a scalar.

    • e.g., 5 m/s.

  • It is always positive.

  • Speed(v)=distancetravelled(d)timetaken(t)Speed \: (v) = \frac{distance \: travelled \: (d)}{time \: taken \: (t)}

  • Since distance is measured in meters, and time is measured in seconds, speed's unit is metres per second (m/s) or kilometres per hour (km/h).

Distance-time graphs

  • Distance-time graphs provide a record of how far an object has moved as time has passed.

  • Distance travelled is plotted on the vertical axis, and time is plotted on the horizontal axis.

  • The line's slope, or gradient, tells us the object's speed.

    • The steeper the line, the greater the speed.

  • Acceleration is when an object speeds up, as shown in diagram C.

  • Other distance-time graphs are also shown in the picture below:

Velocity

  • Unit: m/s (metres per second) or km/h (kilometres per hour).

  • Velocity is speed in a given direction, so it is a vector.

    • e.g., 5 m/s east.

    • We not only know how fast something is going but also where it's going.

  • It can be negative or positive.

  • Velocity:(V)=displacement:(d)time:taken:(t)Velocity \\: (V) = \frac{displacement \\: (d)}{time \\: taken \\: (t)}

  • Displacement means distance travelled in a particular direction from a specified point.

Average speed and average velocity

  • Speed or velocity refers to a specific time/point of a journey.

  • When calculating average speed/velocity, we calculate the speed/velocity of the entire journey.

  • This journey may include the resting time in between and any acceleration or deceleration in the journey.

  • Averagespeed(v)=distancemoved(d)totaltimetaken(t)Average \: speed \: (v) = \frac{distance \: moved \: (d)}{total \: time \: taken \: (t)}

  • Averagevelocity(v)=totaldisplacement(d)totaltimetaken(t)Average \: velocity \: (v) = \frac{total \: displacement \: (d)}{total \: time \: taken \: (t)}

Acceleration

  • Acceleration=(finalvelocity(v)initialvelocity(u))/timetaken(t)Acceleration = (final velocity (v) - initial velocity (u) ) / time taken (t)

  • It is a vector.

  • Acceleration is the rate of increase in velocity with time.

  • It is measured in m/s2m/s^2 (meters per second squared).

  • Deceleration means slowing down.

    • A negative acceleration simply means deceleration.

  • (Finalspeed(vu))2=(initialspeed (vi))2+2acceleration(a)distancemoved(d){(Final \: speed \: (vu))}² = {(initial \: speed \ (vi))}² + 2 * acceleration (a) * distance \: moved \: (d)

Velocity-time graphs

  • The gradient in the picture below is straight, which tells us that the velocity is increasing steadily.

    • This means that the acceleration is uniform.

  • Averagevelocity(v)=initialvelocity(vi)+finalvelocity(vf)2Average \: velocity \: (v) = \frac{initial \: velocity \: (vi) + final \: velocity \: (vf)}{2}

  • The area under a velocity-time graph is equal to the distance travelled by the object in a particular time interval.

Circular motion

  • When an object is travelling in a circle at constant speed, the velocity is always changing as the direction is constantly changing.

  • The resultant force of a circular motion is towards the center of the circle.

2. Forces and Shape

  • The unit used to measure force is the Newton (n).

    • A force of one newton will make a mass of one kilogram accelerate at one metre per second squared.

  • A force is a vector quantity.

Common forces

  • Weight is the pull of the gravitational force on an object.

  • The normal force is a reaction force, the upward push on an object from the ground.

  • Friction is a force that opposes motion.

Balanced and unbalanced forces

  • The resultant force is the sum of all individual forces acting upon an object.

  • When the forces acting on something are balanced, the object does not change the way it is moving.

    • Unbalanced forces acting on an object cause it to change the way it is moving.

  • Inertial mass is a measure of how difficult it is to change the velocity of an object.

    • Inertialmass(m)=force(f)acceleration(a)Inertial \: mass \: (m) = \frac{force \: (f)}{acceleration \: (a)}

Friction

  • Friction is the force that opposes motion between two surfaces in contact.

    • It causes objects moving to slow down and stop.

  • The kinetic energy of the moving object is transferred to heat as work is done by the friction force.

  • Reducing friction means that machines work more efficiently

    • Increasing friction helps tyres grip the road better.

Changing shapes

  • Sometimes, a force can make an object change shape, either permanently or temporarily.

Springs and wires

  • Springs are coiled lengths of certain types of metal, which can be stretched or compressed by applying a force to them.

  • They obey Hooke’s law, which states that the extension is directly proportional to the force causing it.

    • Hooke’s law only applies until the limit of proportionality, after which the object does not obey the law, and the extension is imbalanced.

    • A straight line on a graph of extension shows the object is obeying Hooke’s law.

  • If a spring is stretched beyond its elastic limit, it will not return to its starting length.

  • The extension doubles if two springs are connected to each other directly.

  • The extension halves a load attached to two springs in parallel as the load is shared.

  • Force(f)=mass(m)acceleration(a)Force \: (f) = mass\:(m)*acceleration\:(a)

Elastic bands

  • Elastic bands are another example of changing objects.

    • They do not follow Hooke’s law.

3. Forces and movement

Force, mass, and acceleration

  • The acceleration of an object depends on the size of the unbalanced force and the mass of the object.

  • Acceleration is inversely proportional to mass.

  • Force(f)=mass(m)acceleration(a)Force \: (f) = mass\:(m)*acceleration\:(a)

Human Reaction Time

  • Human reaction time is the time taken between a stimulus being presented and the initiation of a response by an individual.

  • The average human reaction time is 0.25 seconds.

  • Factors Affecting Reaction Time:

    • Age and health of the individual.

    • State of alertness and concentration.

    • Influence of drugs or alcohol.

    • Nature of the stimulus (visual, auditory, etc.).

Stopping Distance

  • Stopping distance is the total distance covered by a vehicle from the moment the driver perceives a hazard until the vehicle comes to a complete stop.

  • Components of stopping distance:

    • Thinking Distance: The distance traveled by the vehicle during the driver's reaction time.​

    • Braking Distance: The distance traveled by the vehicle while the brakes are applied and the vehicle decelerates to a stop.

  • Factors affecting stopping distance:

    • Speed of the vehicle.

    • Road surface conditions (dry, wet, icy).

    • Condition of tires and brakes.

    • Reaction time of the driver.

Weight

  • The weight of an object is the force that acts on it because of gravity.

  • The gravitational field strength is the force that acts on each kilogram of mass.

  • Weight(w)=mass(m)gravity(g)Weight \: (w) = mass\:(m)*gravity\:(g)

  • Gravity on Earth is approximately 9.81N.

Air resistance and terminal velocity

  • Air resistance, or drag, is a frictional force that opposes motion in air. It slows down anything travelling through the air and may also cause the object to heat up.

  • The drag coefficient is a measure of how easily an object moves through the air.

  • Terminal velocity is when the drag force has increased to the point where it exactly balances the weight force.

  • Since there is now no unbalanced force on the object its acceleration is also zero.

Work

  • The work done to stop an object is equal to the initial kinetic energy of the object.

  • KE=Fd=12mu2KE=Fd=\frac{1}{2} mu²

4. Momentum

  • Momentum is a measure of how difficult it is to stop something that is moving.

  • Momentum(p)=mass(m)velocity(v)Momentum \: (p) = mass\:(m)*velocity\:(v)

  • It is a vector quantity, measured in kilogram metres per second (kg m/s).

Momentum and acceleration

  • The rate of change of momentum of an object is proportional to the force applied to the object.

  • Force(F)=finalmomentum(mf)initialmomentum(mi)timetaken(t)Force \: (F) = \frac{final \: momentum \: (mf) \: - \: initial \: momentum \: (mi)}{time \: taken \: (t)}

Momentum and collisions

  • The total momentum of objects that collide remains the same.

Newton’s Laws of Motion

Newton's first law

  • An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.

Newton's second law

  • When a resultant force acts on an object of a constant mass, the object will accelerate in the direction of the resultant force.

  • The product of the mass and acceleration of the object gives the resultant force.

  • Force(f)=mass(m)acceleration(a)Force \: (f) = mass\:(m)*acceleration\:(a)

Newton's third law

  • Every action has an equal and opposite reaction.

  • F1=F2F₁=F₂

    mass1acceleration1=mass2acceleration2mass_1 * acceleration_1 = mass_2 * acceleration_2

5. The turning effect of forces

The moment of a force

  • A moment is the turning effect of a force.

  • They occur when a force causes an object to rotate about a pivot or hinge.

  • The size of the moment is determined by the size of the force and the perpendicular distance from the pivot.

  • Moment(M)=force(f)perpendiculardistancefrompivot(d)Moment \: (M) = force \: (f) * perpendicular\:distance\:from\:pivot\:(d)

  • The unit of moments is Newton Metres (Nm).

  • Opening or closing a door is an example of a moment.

Principle of Moments

  • The Principle of Moments states that for an object to be balanced, the clockwise moment must be equal to the anticlockwise moment.

  • F1D1=F2D2F_1 * D_1 = F_2 * D_2

Centre of Mass and Stability

  • The centre of mass of an object is the point at which the weight of the object acts.

  • For symmetrical objects, the centre of mass is at the point of intersection of its symmetries.

  • When an object is suspended, its centre of mass will come below it.

  • To find the centre of mass of a lamina, it is suspended from a point and a plumb line is hung next to it.

    • A line is drawn using a pencil along the plumb line.

    • This is repeated from multiple points, the point of intersection of the lines is the centre of mass.

  • An object is stable when its centre of mass is above its base.

  • If the centre of mass is not directly above its base, the object will topple over.

  • The lower the centre of mass of an object, the greater the stability.

    • The greater the base area of an object, the greater the stability.