Consider a situation where a motor car (A) with an enginetrouble is being pulled by a breakdown truck (B) on a flat roadas shown in the figure (1). The masses of vehicle A and vehicleB are 1000 kg and 3000 kg respectively. Assume that theresistive force acting on each vehicle against their motion isgiven by 4 N kg-1.(a) Sketch a diagram of the vehicle A on your answer sheet and draw the forces acting on it.When the vehicle B is pulling the vehicle A with a constant velocity of 10 ms-1.(b) Calculate the followed total force applied by the vehicle B?(c) What is the power of the vehicle B?(d) What is the tension in the cable used to pull the car in this situation?
Question
Consider a situation where a motor car (A) with an enginetrouble is being pulled by a breakdown truck (B) on a flat roadas shown in the figure (1). The masses of vehicle A and vehicleB are 1000 kg and 3000 kg respectively. Assume that theresistive force acting on each vehicle against their motion isgiven by 4 N kg-1.(a) Sketch a diagram of the vehicle A on your answer sheet and draw the forces acting on it.When the vehicle B is pulling the vehicle A with a constant velocity of 10 ms-1.(b) Calculate the followed total force applied by the vehicle B?(c) What is the power of the vehicle B?(d) What is the tension in the cable used to pull the car in this situation?
Solution
(a) The forces acting on vehicle A are:
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The gravitational force (weight) acting downwards. This is given by the mass of the car times the acceleration due to gravity (1000 kg * 9.8 m/s^2 = 9800 N).
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The normal force acting upwards. This is equal to the weight of the car, so also 9800 N.
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The resistive force acting against the motion of the car. This is given by 4 N per kg of the car's mass (4 N/kg * 1000 kg = 4000 N).
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The tension force from the cable pulling the car. This is equal to the resistive force (since the car is moving at a constant velocity), so also 4000 N.
(b) The total force applied by vehicle B is the sum of the resistive force acting on both vehicles. This is given by 4 N per kg of each vehicle's mass (4 N/kg * 4000 kg = 16000 N).
(c) The power of vehicle B is given by the work done per unit time. Since work done is force times distance, and distance over time is velocity, we can calculate power as force times velocity. Therefore, the power of vehicle B is 16000 N * 10 m/s = 160000 W or 160 kW.
(d) The tension in the cable used to pull the car is equal to the resistive force acting on vehicle A, which is 4000 N.
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