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Questions on Newton's Laws

Q3. An electric wheelchair, powered by a battery, allows the user to move around independently.

One type of electric wheelchair has a mass of 55 kg.

The maximum distance it can travel on level ground is 12 km when carrying a user of mass 65 kg and travelling at its maximum speed of 1.5 m s–1.

The battery used has an EMF of 12 V and can deliver 7.2 × 104 C as it discharges fully.

(a) Show that the average power output of the battery during the journey is about 100 W.

Time of journey = distance/speed

t = 12 x 103/1.5

t = 8000 s

P = IV

P = QV/t

P = 7.2 × 104 x 12/8000

P = 108 W

 

[3 marks]

(b) During the journey, forces due to friction and air resistance act on the wheelchair and its user.

Assume that all the energy available in the battery is used to move the wheelchair and its user during the journey.

Calculate the total mean resistive force that acts on the wheelchair and its user.

Total energy = power x time

Total energy = 108 x 8000

Total energy = 8.64 x 105J

work done by the wheelchair = F x distance moved

8.64 x 105 = F x 12000

F = 72 N

As there is no acceleration the resistive force must also be 72 N (in the opposite direction)

[2 marks]

(c) The diagram shows the wheelchair and its user travelling up a hill.

The hill makes an angle of 4.5° to the horizontal.

Calculate the force that gravity exerts on the wheelchair and its user parallel to the slope.

mtotal = mwheelchair + mperson

mtotal = 55 + 65

mtotal = 120 kg

weight = mg

weight = 120 x 9.81 N

force parallel to the slope = 120 x 9.81 sin 4.5o

force parallel to the slope = 92 N

[1 mark]

(d) Calculate the maximum speed of the wheelchair and its user when travelling up this hill when the power output of the battery is 100 W.

Assume that the resistive forces due to friction and air resistance are the same as in part (b)

Total resistive force = 92 + 72 = 164 N

Each second 100 J work is done

work done = force x distance moved

100 = 164 x d

d = 100/164

distance moved in one second = speed

speed = 100/164

speed = 0.61 m s-1

[2 marks]

(e) Explain how and why the maximum range of the wheelchair on level ground is affected by:

the mass of the user

the speed at which the wheelchair travels.

Increasing the mass

Reduces the range

Increases the friction on the bearings/tyres

OR

More energy/power is used accelerating the user to the final speed

OR

User and wheelchair have higher KE/ more energy to move

Increasing the speed

Reduces the range

Air resistance increases with speed

[4 marks]

(12 marks Total)