A truck of mass 1750 kg is towing a car of mass 750 kg along a straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 7 - 2013 - Paper 1
Question 7
A truck of mass 1750 kg is towing a car of mass 750 kg along a straight horizontal road. The two vehicles are joined by a light towbar which is inclined at an angle ... show full transcript
Worked Solution & Example Answer:A truck of mass 1750 kg is towing a car of mass 750 kg along a straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 7 - 2013 - Paper 1
Step 1
Find the deceleration of the truck and the car.
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Answer
To find the deceleration of both the truck and the car, we can use the equation of motion:
v2=u2+2as
where:
Final velocity (v) = 14 m s⁻¹
Initial velocity (u) = 20 m s⁻¹
Distance (s) = 100 m
Rearranging the equation:
142=202+2a(100)
Calculating this:
196=400+200a200a=196−400
ightarrow a = -1.02 ext{ m s}^{-2}$$
Thus, the deceleration of both the truck and car is 1.02 m s⁻².
Step 2
Find the force in the towbar.
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Answer
To calculate the force in the towbar, we need to analyze the horizontal forces acting on the car.
Using the equation:
T−300−500extcosθ=0
Substituting the given values (considering cos θ = 0.9):
T−300−500(0.9)=0T−300−450=0T=750extN
Thus, the force in the towbar is 750 N.
Step 3
Find the value of R.
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Answer
Now, to find the value of R, we analyze the horizontal forces acting on the truck:
