Question

A roller coaster cart reaches the 50m high peak of the track with a speed of 23 m/s.Calculate the total mechanical energy of the cart. m=8kg

Answer 1

Given,

The height reached by the cart, h=50 m

The speed of the cart, v=23 m/s

The mass of the cart, m=8 kg

The total mechanical energy of an object is given by the sum of the potential energy and the kinetic energy of the object.

Thus the total mechanical energy of the cart is given by,

`E=\text{mgh}+(1)/(2)mv^2`

Where g is the acceleration due to gravity.

On substituting the known values,

`\begin{gathered} E=8*9.8*50+(1)/(2)*8*23^2 \\ =6036\text{ J} \end{gathered}`

Thus the total mechanical energy of the cart is 6036 J.