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A car of mass 1.8 metric tonnes is moving at a constant speed on a horizontal road.
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If the resistance to the motion is 57.6 kilogramme-weight per tonne of the car’s mass, find the force of its motor.
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To answer this question, let’s recall Newton’s first law of motion.
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Newton’s first law states that an object at rest remains at rest and an object in motion remains in motion with the same velocity unless acted upon by an external force.
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This is sometimes alternatively stated that if the net force — that’s the vector sum of all forces acting on the object — is zero, then the velocity of the object is constant.
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Now our car is indeed moving at a constant speed.
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So this means we know that the net force or the vector sum of all forces acting on the car must be equal to zero.
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So let’s draw a little diagram and see what’s going on.
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In a horizontal direction, the car has two forces acting on it.
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It has a driving force, which acts in the forward direction, and a resistance force.
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Now I’ve labelled this 𝑅.
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But we’re told the resistance of the motion is 57.6 kilogramme-weight per tonne.
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We’re also told the car has a mass of 1.8 metric tonnes.
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And so if the resistance to motion is 57.6 kilogramme-weight per tonne of the car’s mass, then for every 1.8 metric tonnes the resistance is 57.6 times 1.8.
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𝑅 is therefore equal to 103.68 kilogramme-weights.
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Since the speed remains constant, we know that the net force is equal to zero.
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And since it’s moving to the right in our diagram, 𝐹 minus 𝑅 must be equal to zero.
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That is, 𝐹 minus 103.68 equals zero.
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We solve this equation for 𝐹 by adding 103.68 to both sides.
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So 𝐹 must be equal to 103.68 kilogramme-weight.