A car of mass 1500 kg is pulling a trailer of mass 300 kg along a straight horizontal road at a constant speed of 20 m s⁻¹. The system of the car and trailer is modelled as two particles, connected by a light rigid horizontal rod. The power of the car's engine is 6000 W. There are constant resistances to motion of RN on the car and 80 N on the trailer.
- (i)Find the value of R.[2]
- (ii)Find the acceleration of the car and trailer and the tension in the rod at an instant when the speed of the car is 25 m s⁻¹.[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [B1] Using F = P/v Driving force = 6000/20 [= 300 N]
- [B1ft] Net force on system = 300 – R – 220 = 0 ft on DF found R = 300 – 80 = 220
- [M1] Any one equation from the following: Apply Newton's 2nd law to the car / Apply Newton's 2nd law to the trailer / Apply Newton's 2nd law to the system of car and trailer. [New driving force DF = 12500/25 = 500 N]
- [A1ft] Correct DF = 500 must be used. ft on R value found
- [M1] EITHER solve two dimensionally correct simultaneous equations in a and T to find a or T OR solve the system equation to find a [Car: DF-T-R = 1500a, Trailer: T-80 = 300a, System: DF – 80 – R = 1800a]
- [A1] Allow a = 1/9 a = 0.111 m s⁻²
- [A1] Allow T = 340/3 T = 113 N (= 113.3333...)
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