Question

energy exam
in the roller coaster diagram above, at which point would the kinetic energy of the cart be at its highest?

Explanation:

Step1: Recall the relationship between kinetic energy and potential energy

According to the law of conservation of mechanical energy (assuming no non - conservative forces like friction, \(E = K+U\), where \(E\) is the total mechanical energy, \(K=\frac{1}{2}mv^{2}\) is the kinetic energy and \(U = mgh\) is the gravitational potential energy (\(m\) is mass, \(v\) is velocity, \(g\) is the acceleration due to gravity and \(h\) is the height).

Step2: Analyze the height at each point

The gravitational potential energy \(U\) is directly proportional to the height \(h\) (\(U=mgh\)). At point \(c\), the height \(h\) of the roller - coaster cart is the lowest among points \(a\), \(b\), \(c\) and \(d\). Since \(E = K + U\) and \(E\) is constant (assuming no non - conservative forces), when \(U\) is the smallest, \(K\) is the largest.

Answer:

C. c