Modelling assumptions

A football is kicked by the goalkeeper from one end of the football pitch. State the effect of the following assumption on any calculation: The football is modelled as a particle.

• Mass of the object is concentrated at a single point.

• Treat object as having zero mass.

• Rotational forces and air resistance can be ignored.

• Air resistance is modelled as being negligible.

A football is kicked by the goalkeeper from one end of the football pitch. State the effect of the following assumption on any calculation: Air resistance is negligible. Ignore the __________ on the football due to air resistance.

State the effect on the following assumption: An ice puck is hit and slides across the ice and the ice puck is modelled as a particle.

• Ignore rotational effect.

• Don't ignore the effects of air resistance.

• Air resistance plays no role.

• Ignore the effect of any external forces.

State the effect on the following assumption: An ice puck is hit and slides across the ice. The ice is smooth.

• No friction.

• Ignore the friction between puck and ice surface.

• Friction is smooth.

• Friction is rough and there is tension between the ice puck and player.

A parachute jumper wants to model her descent from an aeroplane to the ground. She models herself and her parachute as particles connected by a light inextensible string. Explain why this may not be a suitable modelling assumption for this situation.

Answer explanation

The parachute and jumper should be considered as one particle as they move together.

A fishing rod manufacturer constructs a mathematical model to predict the behaviour of a particular fishing rod. The fishing rod is modelled as a light rod. Describe the effects of this modelling assumption:

• The rod is rigid and has no thickness, hence would be unsuitable for fishing.

• The rod is inextensible.

• The rod has thickness and therefore mass.

• The rod gets affected by air resistance.

The fishing rod is modelled as a light rod. Comment on the validity of this situation.

Answer explanation

If the fishing rod had no thickness and was rigid it would be unsuitable for fishing.

Make a list of the assumptions you might make: The motion of a golf ball after it is hit.

• Model golf ball as a particle.

• Air resistance is important.

• Ignore air resistance.

• Friction of air plays a role.

Make a list of the assumptions you might make: The motion of a child on a sledge going down a snow-covered hill.

• The hill is smooth.

• There is friction.

• The child is a particle

• Buoyancy of the body keeps it above the snow.

Make a list of assumptions you might make: The motion of two objects of different masses connected by a string that passes over a pulley.

• Objects are rigid.

• Particles on ends of a rigid rod.

• Particles attached by inextensible string.

• Pulley is smooth and plays a role in the movement.