Video Transcript
An engine pulls its carriages along a horizontal track at uniform speed. Given that the engine provides a driving force of 2080 kilogram-weight and the
combined mass of the engine and carriages is 250 metric tons, determine the
resistance to their motion per metric ton.
We’re going to model the engine and its carriages as one body. It has a combined mass of 250 metric tons. And the engine provides a forward driving force of 2080 kilogram-weight. We know that there’s some resistance to motion, and we’ll define that to be 𝑅. It acts in the opposite direction to the driving force of the engine.
And finally, whilst we’re not interested in it in this question, we know that there
is a normal reaction force. The engine and its carriages exert a downwards force of their weight on the
floor. The floor itself then exerts a normal reaction force on the engine. So, in order to be able to answer this question, it’s worth noting that the engine is
moving at a uniform speed.
Newton’s first law of motion states that if the net force, or the vector sum of all
forces, acting on the object is zero, then the velocity of that object is
constant. Alternatively, we can say that if it’s moving at a uniform speed, then the vector sum
of its forces must be equal to zero.
Now, in fact, we’re actually only interested in the forces acting horizontally. And we’ll take the direction in which the engine is moving to be positive. Then, the sum of the forces acting in this direction — let’s call that sum 𝐹 sub 𝑥
— is 2080 minus 𝑅. And we are subtracting 𝑅 because it’s acting in the negative direction. Since the sum of the forces is zero, we say that zero is equal to 2080 minus 𝑅. And then adding 𝑅 to both sides of this equation, we find 𝑅 is equal to 2080
kilogram-weight.
Now we’re not quite finished. We have calculated the resistance force that acts on the engine, but we want to
calculate the resistance to motion per metric ton. Since the combined mass of the engine and the carriages is 250 metric tons, the
resistance to motion per ton is found by calculating 2080 divided by 250, which is
8.32. The resistance to motion per ton is 8.32 kilogram-weight.
