P2aL3 Let’s Force it and Balanced forces

Key Words

Acceleration - change in speed divided by time.

Air resistance - drag experienced by moving through air.

Component - a force can be split into two perpendicular force vectors.

Constant velocity - speed in a direction that has the same direction and the same value.

Direction - towards a particular point.

Equal and opposite force - forces that are equal in value but opposite in direction (really?)

Force - push, pull, or twist.

Force meter - instrument to measure force.

Friction - force opposing movement caused by surfaces rubbing against each other.

Mass - amount of material in an object

Resolving - turning a force vector into two perpendicular force vectors.

Resultant force - force that occurs on an object when two or more forces are applied.

Speed - distance divided by the time.

Stationary - something that is standing still.  (NB: Stationery - paper, pens, etc.)

Triangle of forces - a diagram showing the way that three forces act.

Upthrust - upwards force produced by a liquid.

Velocity - speed in a particular direction.

Weight - a force acting on an object caused by gravity.

Test Yourself

Homework
Physics GCSE
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Grade E

You will remember from previous work that:

  • Forces are vectors with a direction as well as a value (or magnitude);
  • Forces are measured in Newtons.

Forces sum to a resultant force:

  • If the forces are in the same direction, they add up;
  • If the forces are in the opposite direction, they subtract.  The direction of the resultant force is the same as the direction of the bigger force.
  • If forces are at right angles, you need to use Pythagoras' Theorem to add the squares.  The resultant is the square root of the number you get.

The resultant force is the single force that would have the same effect as all the forces acting on the object.  We can have as many forces as we like, but they would all sum to a single resultant force.

The forces above have a resultant force, which will result in acceleration in the direction of the resultant force.

 

If the forces are equal and opposite, they are called balanced forces.  That means that the resultant force is zero.  (Note that that does NOT mean that there are no forces; the directions and values of all the forces add up to 0.)  If the forces are balanced, it means that:

  • If an object is stationary, it will stay stationary.

  • If an object is travelling at a constant velocity, it will continue to travel at a constant velocity.

Forces act in pairs.  If you push against a table, it will push against you.  This is Newton's Third Law.

The aeroplane is flying at constant speed in level flight.  There are two pairs of equal and opposite forces:

  • The weight and the upthrust (or lift);

  • The thrust from the engine and the drag (air resistance).

Grade C

If we have two forces that are not in the same direction, or in opposite direction, we can't simply add or take away.  We have to do a vector sum to find the resultant.  This aeroplane is flying with a wind blowing across its path.  It will actually move along the grey arrow, the resultant of the two vectors.

We can show this as a triangle of forces:

 

Let's suppose the aeroplane is flying at 150 m/s and the wind is 20 m/s at 70o to the direction of the flight.

We can work out the resultant by accurate drawing on graph paper.  Choose a scale of 1 cm = 10 m/s.  Draw the horizontal vector velocity as a line exactly 15 cm long.  Draw the wind velocity as a vector exactly 2 cm long, and use a protractor to draw an angle of 70 o.

On measuring the resultant, we see that the line is 14.4 cm.  Since 1 cm = 10 m/s, the speed of the aeroplane relative to the ground is 144 m/s.

We can resolve any force vector going in any direction as the resultant of two perpendicular force vectors.  We resolve the force into its components.

If an object is going down a slope, there are two components, but they are NOT horizontal or vertical, because the weight always acts vertically downwards.  The weight is the resultant of two force vectors:

  • The downhill force, parallel to the slope;
  • The force at 90o to the ground, often called the normal force or the reaction force.

When objects are moving, the idea of forces acting in pairs still applies.  If a car pulls a trailer with a force of 1500 N, the trailer is pulling on the car with a force of 1500 N.  When the car accelerates, the force on the trailer might increase to 2000 N.  The pulling force on the car from the trailer is 2000 N as well.

Guns recoil because forces act in pairs.  Since F = ma, the force that acts on the bullet is the same force acting on the gun (and the hunter).  The hunter and gun have a much bigger mass so a lower acceleration.  We can also use the concept of momentum to describe the recoil.

 

Grade A

We can resolve forces without needing to do accurate drawing (which might not be all that accurate).  Instead we use trigonometry.   Let us go back to the object on a slope:

The weight is W.  Weight is a force worked out by multiplying the mass (kg) by the acceleration due to gravity ( = 10 m/s2). 

W = mg

Therefore the two components are:

  • Downhill force W sin q;

  • Normal force W cos q.

The strange looking symbol q is "theta", a Greek letter 'th', which is often used to show an angle.

 

When a rocket is accelerating upwards, it exerts a force on each cosmonaut in it.  They in turn exert an equal and opposite force.  This force may be five times their weight, so they feel very heavy.  They are trained in various machines like a centrifuge in order to know what to expect.

They sit in the capsule and are spun round on the giant machine.  It is not a pleasant ride. 

People also pay large sums of money to go on fairground rides that do similar things.  As does a baby bouncer: