4th form: Motion & Forces

Scalars and Vectors Measurable quantities can be divided into scalars and vectors. Scalar quantities have a magnitude (size) only Examples? Mass, distance, speed, time... Vector quantities have both a magnitude and a direction associated with them Force, displacement, velocity...

Adding scalars and vectors Adding scalar quantities is easy, just add the magnitudes eg if it takes 15 minutes to eat lunch and you have a further 45 minutes before lessons, how long was the break? Adding vectors, we have to take the direction of the quantities into account eg pushing a car against friction

Adding vectors

Adding vectors (more generally) The resultant R is found by combining all the component vectors together It is the single vector which is equivalent to the action of all the component vectors This is A-level stuff...

Speed: a reminder Speed is a measure of how quickly something is moving Actually, the above formula really tells you the average speed during the time interval As the time interval gets smaller, you get closer to calculating the instantaneous speed.

Displacement-time graphs Try to describe the motion shown in the graph What does the slope of the line represent? What does the slope of the dotted line tell you?

Displacement-time graphs Constant speed backwards Constant speed forward Slope=average speed of return journey stationary Slope = speed Speed=5/0.42=11.9 km/h After 160 minutes, we are back where we started

Calculating speed The slope of the graph gives the speed (strictly the velocity) The steeper the line, the higher the speed (a) Slope = 60/10 = 6.0 m/s (b) (b) Slope = 0/5 = 0.0 m/s (a) (c) (c) Slope = -100/25 = -4.0 m/s (d) (d) Slope = 40/15 = 2.7 m/s

Displacement-time graphs How would you represent something getting slower? t x Note: distance can also become negative, if object travels in the opposite direction

Speed and Velocity The velocity of an object gives its instantaneous speed and direction (This is called a VECTOR) As with displacement, the sign of the velocity indicates the direction a negative velocity means speed in the opposite direction

Speed and Velocity Going from A to B: + velocity Going from C to F: - velocity

Velocity-time graphs Try to describe the motion shown in the graph What does the slope of the line represent? Where is the object not moving?

Velocity-time graphs Constant speed forwards Constant acceleration Gradual slowing More rapid slowing stationary Reversing direction and speeding up Slowing to a stop Constant speed backwards

Acceleration Acceleration is the rate of change of velocity If you are speeding up, acceleration is + If you are slowing down, acceleration is - m/s s m/s2

Acceleration is the slope of the velocity graph Acceleration = (v-u)/t So for this region: a= 8/4 = 2 m/s2 and for this region: a= 0/6 = 0 m/s2 (constant v)

What about the displacement? Displacement = velocity × time i.e. the area under the graph So in the first 4s: In the next 6 seconds

Tachographs A tachograph is an instrument which records the velocity-time graph of a vehicle. It is used to check that EU regulations limiting the time lorry and bus drivers can spend at the wheel are obeyed 9 hours/day 45 minute break every 4.5 hrs.

Forces: a reminder A force is a “push” or a “pull”. Unit: newton (N) Forces arise due to the interaction of two (or more) objects. Not all forces require contact, some can act at a distance e.g. gravity, magnetism Forces are vectors, Direction matters

Weight: a reminder “Mass” is a measure of how much “stuff” an object contains measured in kg “Weight” is the force that object exerts due to the effect of gravity measured in newtons (N) So an astronaut has the same mass on Earth or the Moon, but his weight will be different On Earth, g ≈10 N/kg gravitational field strength weight mass

Representing forces Forces can be represented with arrows, whose length indicates the size of the force.

Force diagrams A free body diagram can be very useful to analyse the forces acting on an object We draw it isolated from its surroundings and show all the forces acting

What forces are acting here? Draw on as many as you can think of… Tension in the rope Push and friction (for each person) Weight and reaction (for each person)

Combining forces If several forces act on an object, we can work out the equivalent single resultant force by adding them up, taking direction into account. What is the resultant? 4 newtons downwards How about these? 7 N 6 N 3 N 4 N 1 N 5 N 4 N 4 N 4 N 0 N

Newton’s 1st law Balanced forces It is possible to have all forces balanced, so the resultant = 0. In this case, no resultant force acts and the object continues to move at constant velocity (or remain stationary if it wasn’t moving). For a plane flying at constant speed and height: Thrust = drag Lift = weight

Newton’s 1st Law A body will remain at rest or, if moving, continue to move at a constant velocity, unless acted on by a force.

Unbalanced forces If the resultant force is not zero, a net force is acting on the body and its motion will change. It will accelerate in the direction of the force. thrust > drag and lift > weight, so aeroplane accelerates and takes off

Force causes acceleration Newton’s 2nd law Force causes acceleration When a force acts on a body, it changes its velocity If no resultant force acts, there is no acceleration (Newton’s 1st law) Remember, acceleration can mean a change of speed or direction 1 N is the force which accelerates 1 kg at 1 m/s2 force mass acceleration

F=ma So: For a given mass, a bigger force produces a bigger acceleration For a given force, a smaller mass experiences a bigger acceleration

Force, mass and acceleration A force of 1000 N is applied to push a mass of 500 kg. How quickly does it accelerate? A force of 3000N acts on a car to make it accelerate by 1.5 m/s2. How heavy is the car? A car accelerates at a rate of 5 m/s2. If it weighs 500 kg how much driving force is the engine applying? A force of 10 N is applied by a boy while lifting a 20 kg mass. How much does it accelerate by?

Remember Weight? We had where W was the weight – the force due to gravity Now we know gravitational field strength Acceleration due to gravity On Earth: g ≈10 N/kg, a ≈10 m/s2

Investigating F, m and a We can measure acceleration with light gates What happens as you vary: The mass on the hanger? The mass of the trolley? Why do we need a ramp? How do we set the right angle?

What do we find? acceleration is proportional to force acceleration is inversely proportional to force a a F a a 1/m

Horizontal motion Driving force < counter force: vehicle slows down Driving force – provided by rider/engine Counter force – air resistance and friction Driving force < counter force: vehicle slows down Driving force = counter force: vehicle moves at constant velocity Driving force > counter force: vehicle speeds up

Falling Objects An object falls because of its weight (force due to gravity) When object falls freely – no other forces act on it so resultant force is just its weight. Remember F = ma? Acceleration of 10m/s2 is constant for all objects.

Classic experiment So if we dropped a hammer and a feather at the same time, which would hit the ground first? Why? Hammer & Feather

Drag Objects moving in a fluid have drag force. For objects travelling through the air we call this drag force air resistance. Air resistance increases with speed. So as a falling object speeds up, the resultant force decreases. This means the acceleration decreases.

Reaching a constant velocity Object reaches a constant velocity when the drag force/air resistance is equal & opposite to its weight. Resultant force = zero Acceleration = zero Velocity = terminal velocity

Why does a car have a top speed? The AR 8C has a 4.7 litre 450 bhp (340 kW) engine to provide driving force. Force means acceleration, so why can’t the car accelerate forever?

What determines terminal velocity? Frontal area Shape Mass Surface

Balanced Forces = Constant Velocity

Stages of a parachute jump

Just after letting go... Velocity =0 Drag = 0 Force = weight Acceleration = g

Falling quite fast now... Velocity is high Drag is large Force < weight Acceleration < g

Falling at a constant speed... Velocity constant Drag = weight Force = 0 Acceleration = 0

Pull the ripcord... Velocity still high Drag > weight Force upwards Acceleration upwards (so speed of fall decreases)

Drift downward... Velocity constant (slower) Drag = weight Force = 0 Acceleration = 0

Terminal Velocity

Label the graph

Urban Myth? So, would a penny dropped from a skyscraper kill someone it hit at the bottom? See here for the answer (also here if you wonder about bullets coming down)

Springs: a reminder We have seen that springs obey Hooke’s Law: The extension is proportional to the force applied (up to some limit)

Other “stretchy” things Hooke’s Law also applies to other objects... Metal bars, wires, bones, even glass! ...up to a point If you go beyond that point you may get failure (snap) or permanent deformation (doesn’t return to original shape) Hooke’s Law limit

Rubber bands Rubber bands are elastic, can be stretched and return to their original length, BUT they do not obey Hooke’s Law How can you tell? Describe how it stretches...