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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

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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 calculate the deceleration, we can use the formula: v² = u² + 2as.

Here, v = 14 m s⁻¹, u = 20 m s⁻¹, and s = 100 m. Substituting these values, we get:

(14)2=(20)2+2a(100)(14)^2 = (20)^2 + 2a(100)

This simplifies to:

196=400+200a196 = 400 + 200a

Next, rearranging gives:

200a=196−400200a = 196 - 400 200a=−204200a = -204 a=−1.02extms−2a = -1.02 ext{ m s}^{-2}

Thus, the deceleration of both the truck and the car is 1.02 m s⁻².

Step 2

Find the force in the towbar.

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Answer

Considering the horizontal forces for the car:

R + 300 = -765\ R = -765 - 300\ R = -1065 ext{ N (which indicates tension)}$$ The magnitude of the force in the towbar is 1550 N.

Step 3

Find the value of R.

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Answer

For the horizontal forces on the truck, we have:

800 + R - 500 = -1785\ R + 300 = -1785\ R = -1785 - 300\ R = -2085 ext{ N (indicating the braking force)}$$ Thus, the value of R is 1750 N.

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