Question

A cart on frictionless rollers approaches a smooth, curved slope h = 0.45 meters high. What minimum speed v is required for the cart to reach the top of the slope?

Answer 1

Given data

*The given height is h = 0.45 m

*The value of the acceleration due to gravity is g = 9.8 m/s^2

The formula for the minimum speed (v) required for the cart to reach the top of the slope is given by the conservation of energy as

`\begin{gathered} U_k=U_p \\ (1)/(2)mv^2=mgh \\ v=\sqrt[]{2gh} \end{gathered}`

Substitute the known values in the above expression as

`\begin{gathered} v=\sqrt[]{2*9.8*0.45} \\ =2.96\text{ m/s} \end{gathered}`

Hence, the minimum speed (v) required for the cart to reach the top of the slope is v = 2.96 m/s