Explain why the power of a train's engine must be increased to maintain the speed while travelling up a slope

the power (outside) of the train must be increased for the increase in resistance by the weight component.

Explanation:

We analyze the movement of the train at constant speed, on flat ground the force of the motor must counteract the friction force that opposes the movement, therefore to maintain the constant speed the two forces must be of the same magnitude.

When the train goes up a slope, it is subjected to two forces: the friction force that opposes the movement and a component of the weight in the opposite direction to the movement, therefore the power (outside) of the train must be increased for the increase in resistance by the weight component.

the first american roller coaster was the mauch chunk switchback railway, built in the mountains of pennsylvania in the mid-1800s. the track, originally built to send coal to a railway, was reconfigured as a "scenic tour."

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explanation:

no diagram was provided, but i'm guessing it's the one i've attached to my answer.

here, a mechanical force turns the rod.   this generates an electric current in the coil, which powers the bulb.