1.6 Free body force diagrams describing complex force situations involving moving objects

(a)  A 'free body force diagram' of a cyclist showing all the forces acting on the body (not to a force scale)

A 'free body force diagram' should show every force acting on an isolated object (body) or system but shows none of the forces it exerts on the surroundings.

The following examples assume the object is moving at a constant velocity.

The size of the arrows should indicate the relative magnitude (size) of the force.

There are four forces acting on the body (= bike + cyclist):

F1 is the air resistance due to friction between the surface of the bike + cyclist combination and the air, also friction between the wheels and road, and, friction in moving parts of the bike.

All three friction forces combined oppose the forward motion of the bike and rider.

 

F3 is the thrust or push of the bike from the power generated by the cyclist.

If F1 = F3 the cyclist continues at the same speed and direction - constant velocity, net resultant force of zero.

If F3 > F1 the cyclist accelerates - speeds up, net resultant force = F3 - F1

and, if F1 > F3 the cyclist decelerates - slows down, net resultant force = F1 - F3

See Newton's 1st law of motion.

 

F2 is the weight of the bike + cyclist combination due to the Earth's gravity field effect, weight of object acting on the road with the normal contact force

 

F4 is the normal contact force of the atoms of the road surface pushing back up on the bike.

If the bike and rider are moving along smoothly without jumping up or down, F2 = F4, net resultant force of zero.

(b)  A 'free body force diagram' of a swimmer showing all the forces acting on the body (not to a force scale)

F1 is the water resistance due to friction between the swimmer and the water

 

F2 is the weight of the swimmer acting on the water

 

F3 is the thrust or push of the swimmer from the power generated by the swimming action

 

F4 is the upthrust of the water on the swimmer (buoyancy effect)

When F1 = F4 the swimmer floats at an average stable height above the water.

When F2 = F3 the swimmer moves at more or less a constant speed.

In both cases there is a slight variation due to the swimming stroke cycle.

(c) A 'free body force diagram' of a parachutist showing all the forces acting on the body (not to a force scale)

F1 is the air resistance (drag effect) due to friction between the parachutist and the air.

F2 is the weight of the parachutist due to gravity, 'pulling' the parachutist downwards.

If F1 = F2 the parachutist will fall at a constant speed, a constant velocity if no side wind.

F3 is a push on the parachutist by a side wind.

If it is zero the parachutist will fall vertically.

Note that the parachutist can pull on the cords of the chute to alter the direction of the drag effect to manoeuvre into a safe and intended landing location!

(d) A skier in action

Skiing involves the forces of:

F1 = weight (gravity force acting on skier).

F2 = friction - resistance to the forward motion (friction between snow and ski) AND the air resistance (friction between skier's clothing and the surrounding atmosphere brushing over the surface).

F3 = the forward thrust force from gravity causing the downhill motion of the skier.

F4 = force of snow from its compression.

This is a similar situation to the situation of examples (a) the cyclist and (b) the swimmer, assuming a constant velocity.

Draw this one for yourself and which forces are equal at constant velocity?

(e) A 'free body force diagram' of a moving bus showing all the forces acting on the body (not to a force scale)

F1 is the compressed ground force pushing up against the weight of the bus.

F2 is the weight of the bus due to the Earth's gravitational field.

F3 is the thrust force from the engine of the bus.

F4 is the resistance force from the friction of the wheels on contact with the ground and the air resistance as the air is brushed over the surface of the bus. There is also friction from the moving parts of the engine.

When F3 = F4 the bus will travel at a steady constant speed or velocity.

If the driver takes their foot of the accelerator pedal or applies the brakes, F4 > F3 and the bus slows down. Applying the brake considerably increases the force of friction opposing the forward movement of the bus.

If the driver presses down harder on the accelerator pedal to increase the thrust, then F3 > F4 and the bus will increase in speed of velocity.

As the bus speeds up, the friction (with air or road contact) increases and this continues until again F3 = F4 when the bus will once again travel at a constant speed or velocity.

In diagrams to resolve numerical problems, the length of the arrow should equal the magnitude of the force OR a numerical force value indicated on the arrow.

 

See also 3. Calculating resultant forces using vector diagrams and work done calculations