P2.2 - Newton's Laws

• Contact force:

  To exert a contact force, two objects must be touching, for example pushing or pulling an object.

  Friction is a contact force as an object is being pushed along a surface, there will be friction acting on it in the opposite direction.
• Non - contact force:

  Non-contact forces are forces between two objects that aren't touching. For example, electrostatic, magnetic and gravitational forces.
• Interaction pair:

  An interaction pair is a pair of equal and opposite forces acting on two different objects. E.g. if a person leans against a wall, the person pushes on the wall and the wall pushes back on the person. The forces on the person and the wall are equal and opposite. This is an example of Newton's Third Law
• Resultant force: the overall force on a point or object.


  In most real situations there are at least two forces acting on an object along any direction.

  The overall effect of the forces decide whether the object accelerates, decelerates or has a steady speed.

  If a number of forces act at a single point, you can replace them with a single force called the resultant force. It has the same effect on the motion as the original forces acting altogether.

  If the forces all act along the same line the resultant force is found by just adding or subtracting them.
• Resultant force:

  The diagram on the right shows a ball falling. Weight and air resistance are acting along the same line, so the resultant force acting on the ball = weight - air resistance 8-35 N in the downwards direction.

  
• Free body force diagram:

  Forces are vectors so they have a size and direction. A free body force diagram is a diagram of an object with arrows drawn to show the direction and size of the forces acting on the object.
• A Resultant Force of Zero:

  A resultant force of zero means all the forces are balanced

  An object with a zero resultant force will either be stationary or moving at a steady speed.
• This diagram shows an apple sat on a table. The force due to gravity is acting downwards. The apple isn't moving because there's another force of the same size acting in the opposite direction to balance the weight. This is the normal contact force from the table top pushing up on the apple.

  
• Non-Zero Resultant:

  A non-zero resultant force means the forces are unbalanced

  If there's a non-zero resultant force on an object, then it will either accelerate or decelerate. This is because the forces are unbalanced.
• In the example of the car, the thrust is greater than the drag, so the car is accelerating. If the drag was greater than the thrust, the car would decelerate. The normal contact force and the weight acting on the car balance each other (otherwise the car would go flying off or sink through the road).

  
• Use Scale Drawings to Find the Resultant Force:

  Resultant force can also be called the net force.

  You can find the size and direction of the resultant force on an object using scale drawings. Draw the forces acting on the object to scale and 'tip-to-tail', then measure the length of the resultant force on the diagram. This is the line drawn from the start of the first force to the end of the last force.

  A) resultant

  B) vector diagrams

  
• Equilibrium:

  An object is in equilibrium if all the forces on it are balanced. When an object has a zero resultant force, it is in equilibrium. All the forces on the object cancel each other out. You can use scale drawings to demonstrate this. For example, look at the scale drawing of the three forces that are acting on the object. If you draw all the forces tip-to-tail, you can see that they create a loop, so the resultant force is zero. The object is in equilibrium.

  
• Resolving Vector:

  • When you resolve a force, you split the force into two forces that are at right angles to each other. The two forces have the same overall effect as the original force.
  • You can resolve a force using a scale drawing - just draw two lines so that the original force becomes the longest side of a right-angled triangle.
  • Resolving forces is useful when you need to see the effect of a force along a particular line.
• Resolving forces example:

  A toy train is being pulled along a track by a rope at an angle to the track. The scale drawing shows this force and the direction the train is moving.

  The force can be resolved into a force acting horizontally and a force acting vertically. Draw a right-angled triangle. The size of the vertical force is found by measuring the length of the vertical part of the triangle.

  The size of the force acting horizontally can also be found by measuring the length of the horizontal part of the triangle. 2 N = size of force pulling train in direction of movement.

  
• Newton's First Law:

  An object will remain stationary or at a constant velocity unless acted upon by an external force.if the resultant force on a stationary object is zero, the object remains stationary, there has to be a resultant force to get them started. No resultant force on a moving object means it'll carry on moving at the same velocity - for an object to travel with a uniform velocity, there must be zero resultant force.Non-zero resultant force means the object will accelerate in the direction of the force: starting, stopping, speeding up, slowing down and changing direction.
• Newton's Second Law: A Non-Zero Resultant Force Causes an Acceleration


  Newton's Second Law says:

  The force acting on an object is equal to its rate of change of momentum. This means any resultant force will produce an acceleration, and the formula for it is:

  force (N) = mass (kg) × acceleration (m/s²) or F = ma

  The F is always the resultant force.
• Acceleration of a trolley on an air track demonstrates Newton's Second Law:

  The force acting on the trolley is equal to the weight (W = M X g) of the hanging mass.

  The hanging mass is released, pulling the trolley along the track.

  By measuring the time and speed at which the trolley passes each light gate, its acceleration can be calculated.

  Increase the force acting on the trolley by moving one of the masses from the trolley to the hanging mass, and repeating the experiment.

  Plot your results on a graph of force against acceleration, you should get a straight line, as F = ma.

  
• Friction:

  When an object is moving, friction acts in the direction that opposes movement.

  Friction makes things slow down and stop, so you need a driving force to keep moving (thrust).

  If driving force is equal to the friction force, object will move at steady speed.

  If driving force is greater than friction force, object will accelerate. If driving force is less than friction force, object will decelerate.

  Friction occurs between two surfaces in contact (e.g. tyres and the road), and drag occurs when object passes through fluid (e.g. a boat through water). Air resistance is a type of drag.
• Terminal velocity:

  When objects first set off they have more driving force than friction force (resistance), so they accelerate.

  But the resistance is directly proportional to the velocity of the object - resistance ∝ velocity. So as the velocity increases, the resistance increases as well. This gradually reduces the acceleration until the

  friction force is equal to the driving force so it doesn't accelerate any more. The forces are balanced (there's no resultant force). The object will have reached its maximum velocity or terminal velocity.
• Drag

  The greater the drag (or air resistance or friction), the lower the terminal velocity of an object, and drag depends on the object's shape and area.
• Drag on skydiver:

  The driving force for a skydiver is his weight due to gravity and the drag (air resistance) depends on the skydiver's shape and area.

  Without his parachute open, a skydiver's area is quite small. His terminal velocity is about 120 mph. With the parachute open, there's more air resistance (at any given speed) because the skydiver's area is larger, but the driving force (his weight) is the same. This means his terminal velocity is much smaller (~15 mph), which is a safe speed to hit the ground at.

  Decreasing drag makes things faster - streamlined cars have less drag
• Skydiver:

  A) resistance

  B) weight

  C) speed

  D) =

  
• Terminal velocity on skydiver:


  1.A skydiver accelerates as weight due to gravity is greater than air resistance.

  2.But air resistance increases as velocity increases until weight = air resistance, and they reach terminal velocity.

  3.The parachute opens and weight is less than air resistance, so they decelerate.

  4.As velocity decreases, the air resistance also decreases until weight = air resistance they reach a new terminal velocity.

  A) terminal velocity

  
• To find the terminal velocity of a toy parachute drop it from a sensible height in front of an object with regular vertical markings at set heights (e.g. markings on a wall), and measure the time at which it falls past each marking. Use the differences between times to find its average velocity between each pair of markings and plot your results on a graph of velocity against time. It should have a curved shape.
• Inertia:

  Inertia is the measure of how difficult it is to change an object's velocity.

  It is dependent on the inertial mass of the object.

  Inertial mass is defined as the ratio of the force over acceleration: inertial mass = force / acceleration

  This is just the rearranged equation for Newton's Second Law.

  A larger inertial mass requires a larger force to accelerate by a certain amount.
• Newton's Third Law says that:

  When two objects interact, the forces they exert on each other are equal and opposite.

  That means if you push something, say a shopping trolley.

  the trolley will push back against you, just as hard.

  And as soon as you stop pushing, so does the trolley.

  The two forces are acting on different objects.
• Newton's third law - pair of ice skaters:

  When skater A pushes on skater B (the 'action' force), she feels an equal and opposite force from skater B's hand (the 'reaction' force).

  Both skaters feel the same sized force, in opposite directions, and so accelerate away from each other.

  Skater A will be accelerated more than skater B, though, because she has a smaller mass, so a smaller inertia a=F/m (from rearranging Newton's Second Law).

  
• Newton's third law with an object in equilibrium:

  Imagine a book sat on a table:

  The weight of the book pulls it down, and the normal reaction force from the table pushes it up. This is NOT Newton's Third Law. These forces are different types and they're both acting on the book.

  The pairs of forces due to Newton's Third Law in this case are:

  The weight of book is pulled down by gravity from Earth (W1) and the book also pulls back up on the Earth (W2).

  The normal contact force from the table pushing up on the book (R1) and the normal contact force from the book pushing down on the table (R2).

  
• Momentum:

  The greater the mass of an object and the greater its velocity, the more momentum the object has. They're linked by this equation:

  momentum (kgm/s) = mass (kg) x velocity (m/s) or p = m X v

  Momentum is a vector - it has size and direction.
• Change in momentum:

  When a resultant force acts on an object for a certain amount of time, it causes a change in momentum. Newton's 2nd Law can explain this:

  A resultant force on an object causes it to accelerate: force = mass × acceleration.

  Acceleration is just change in velocity over time, so: force = mass X change in velocity / time

  This means a force applied to an object over any time interval will change the object's velocity.

  Mass x change in velocity is equal to change in momentum, so you end up with the equation: force (N) = change in momentum (kg m/s) / time (s) or F = P/t
• Change in momentum in collisions:

  The faster a given change in momentum happens, the bigger the force causing the change must be

  (i.e. if time gets smaller, Force gets bigger). So if someone's momentum changes very quickly, like in a car crash, the forces on the body will be very large, and more likely to cause injury.

  Changes in momentum in collisions in terms of acceleration - a change in momentum normally involves a change in velocity, which is what acceleration is. Force = mass × acceleration, so the larger the acceleration (or deceleration), the larger the force needed to produce it.
• law of conservation of momentum:


  In a collision when no other external forces act, momentum is conserved i.e. the total momentum after the collision = total momentum before the collision

  1. Imagine a red snooker ball rolls towards a stationary yellow snooker ball with the same mass. If after the collision, the red ball stops and the yellow ball moves off, then the yellow ball will have the same velocity as the original velocity of the red ball (assuming there's no friction).
• Conservation of momentum also explains rocket propulsion:


  When a rocket is stationary, it has zero velocity and so zero momentum. If the rocket's engines then fire, it'll chuck a load of exhaust gases out backwards (negative momentum). Since momentum is always conserved, this means the rocket has to move forwards (positive momentum), in order to keep the combined momentum of the gases and the rocket at zero.
• If two objects collide and join together, then the total momentum of both objects before the collision = momentum of the combined object after the collision.
• Collisions can be Elastic or Inelastic:


  Momentum is conserved in both elastic and inelastic collisions.

  An elastic collision is where the total energy in the kinetic energy stores of the objects colliding is the same before and after the collision - i.e. the energy in the kinetic energy stores is conserved.

  An inelastic collision is where some of the energy in the kinetic energy stores is transferred to other stores. For example, energy can be transferred away by heating or by sound.
• Work done:


  When a force makes an object move, energy is transferred and work is done. Whenever something moves, something else is providing some sort of effort to move it. The thing putting the effort in needs a supply of energy (from fuel or food or electricity etc.). It then does work by moving the object, and transfers the energy it receives (from fuel) to other stores. Whether this energy is transferred usefully (e.g. by lifting a load) or wasted (e.g. dissipated by heating from friction), you still say that 'work is done'. 'Work done' and 'energy transferred' are the same.
• The formula to calculate the amount of work done is:

  work done (J) = force (N) × distance (m) or W = F x d

  The distance here is the distance moved along the line of action of the force (i.e. the distance moved in the direction of the force).
• If a force is applied to move an object, the work done on the object will be equal to the energy transferred to the kinetic energy store of the object if there's no friction.

  If an object is already moving and then a force (such as friction) slows it down, the energy transferred from the object's kinetic energy store is equal to the work done against the object's motion.

  Work done on an object can also be transferred to other energy stores. E.g. the work done on lifting an object off the ground will be equal to the energy transferred to its gravitational potential energy store.
• Power:

  Power is a measure of how quickly work is being done. As work done = energy transferred, you can define power like this: Power is the rate at which energy is transferred.

  So, the power of a machine is the rate at which it transfers energy. For example, if an electric drill has a power of 700 W this means it can transfer 700 J of energy every second.

  Formula for power:

  power (W) = work done (J) / time (s) or P =W/t

  The proper unit of power is the watt (W). 1W = 1 J of energy transferred per second (J/s).
• Work done is sometimes given in Nm (newton meters), but it's the same as J, so converting between the two is easy, i.e. 5 Nm = 5 J.