read the scenario and solve these two problems. when traveling at top speed, a roller coaster train with a…
read the scenario and solve these two problems. when traveling at top speed, a roller coaster train with a mass of 12,000 kg has a velocity of 30 m/s. the kinetic energy of the train at top speed is j. given this kinetic energy, what is the tallest hill this roller coaster train can reach the top of? the train can climb a hill that is m high.
Answer
Explanation:
Step1: Calculate kinetic energy
The formula for kinetic energy is $K.E.=\frac{1}{2}mv^{2}$, where $m = 12000$ kg and $v = 30$ m/s. $K.E.=\frac{1}{2}\times12000\times30^{2}$ $K.E. = 6000\times900$ $K.E.=5400000$ J
Step2: Calculate height of hill
At the top of the hill, all the kinetic - energy is converted to potential energy $P.E.=mgh$. We know $P.E. = K.E. = 5400000$ J, $m = 12000$ kg and $g = 9.8$ m/s². We can solve for $h$ from the formula $h=\frac{P.E.}{mg}$. $h=\frac{5400000}{12000\times9.8}$ $h=\frac{5400000}{117600}\approx46$ m
Answer:
The kinetic energy of the train at top speed is 5400000 J. The train can climb a hill that is 46 m high.