Question (16 marks)
An electric wheelchair powered by a 12 V battery has a maximum speed of 1.5 ms-1 on level ground. The maximum useful driving power of the motor and transmission system is 30 W. The efficiency of the system is 70%.
(a) Explain briefly why all modes of transport have a maximum speed which depends on the power output of the propulsion system. (3 marks)
(b) For the maximum speed, calculate:
(i) the power supplied by the battery; (2 marks)
(ii) the current in the motor circuit. (2 marks)
(c) Air resistance is negligible at 1.5 1.5 ms-1. Show that the resistance due to friction in the moving parts of the wheelchair is 20 N. (2 marks)
(d) So that wheelchair users can have access to the same facilities as others, buildings such as schools are fitted with ramps which enable the wheelchairs to be used.
One such ramp has a gradient that rises 0.12 m for every metre moved along the ramp, as shown in the figure below:
The total mass of a wheelchair and a student is 110 kg.
The acceleration of free fall, g = 9.8 ms-2
(i) Calculate the component force in the direction shown by the arrow R because of the weight of the wheelchair and student. (2 marks)
(ii) Assuming that the resistance due to frictional forces is still 20 N, calculate the maximum speed of the wheelchair up the ramp. (2 marks)
(e) A designer has to consider a number of physical factors when choosing the material for the ramp when designing it. State and explain briefly two important physical factors which should be considered.
Factor 1:
Factor 2:
(3 marks)
(b) For the maximum speed, calculate:
(i) the power supplied by the battery; (2 marks)
(ii) the current in the motor circuit. (2 marks)
(c) Air resistance is negligible at 1.5 1.5 ms-1. Show that the resistance due to friction in the moving parts of the wheelchair is 20 N. (2 marks)
(d) So that wheelchair users can have access to the same facilities as others, buildings such as schools are fitted with ramps which enable the wheelchairs to be used.
One such ramp has a gradient that rises 0.12 m for every metre moved along the ramp, as shown in the figure below:
The total mass of a wheelchair and a student is 110 kg.
The acceleration of free fall, g = 9.8 ms-2
(i) Calculate the component force in the direction shown by the arrow R because of the weight of the wheelchair and student. (2 marks)
(ii) Assuming that the resistance due to frictional forces is still 20 N, calculate the maximum speed of the wheelchair up the ramp. (2 marks)
(e) A designer has to consider a number of physical factors when choosing the material for the ramp when designing it. State and explain briefly two important physical factors which should be considered.
Factor 1:
Factor 2:
(3 marks)
Answer
(a) Resistive force increases with speed; work done against this force; speed max. when no resultant force/forces in equilibrium;
(b)(i) Efficiency = useful output power/input power; P = 30/0.70 = 43 W;
(b)(ii) Power = VI; I = 43/12 = 3.6 A;
(c) Power = Fv; F = 30/1.5; (= 20 N)
(d)(i) F = mg sin θ; (= 110 x 9.81 x 0.12/1) = 129 or 130 N;
(d)(ii) Total resistive force = 129 + 20 = 149 N; (power = Fv) v = 30/149 = 0.2(0) ms-1;
(e) Strength; support considerable weight; tough; to prevent fracture; thickness; for strength; friction; to get grip; low mass; allow movement to new place; corrosion resistant; to avoid long term problems;
(b)(i) Efficiency = useful output power/input power; P = 30/0.70 = 43 W;
(b)(ii) Power = VI; I = 43/12 = 3.6 A;
(c) Power = Fv; F = 30/1.5; (= 20 N)
(d)(i) F = mg sin θ; (= 110 x 9.81 x 0.12/1) = 129 or 130 N;
(d)(ii) Total resistive force = 129 + 20 = 149 N; (power = Fv) v = 30/149 = 0.2(0) ms-1;
(e) Strength; support considerable weight; tough; to prevent fracture; thickness; for strength; friction; to get grip; low mass; allow movement to new place; corrosion resistant; to avoid long term problems;
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