# What minimum speed does a 300 g puck need to make it to the top of a 0.12 m long, 34.74 degrees...

## Question:

What minimum speed does a 300 g puck need to make it to the top of a 0.12 m long, 34.74 degrees frictionless ramp?

## Conservation of Energy:

When no external forces are acting on an object, we can observe the law of conservation of energy on an object. This law states that the sum of the potential and kinetic energies are the same at two points in a system, or {eq}\displaystyle \sum E_i =\sum E_f {/eq}.

Determine the speed of the puck, {eq}\displaystyle v {/eq}, by equating the initial kinetic energy, {eq}\displaystyle E_{kin}= \frac{1}{2}mv^2 {/eq} where {eq}\displaystyle m {/eq} is the mass of the puck, to the potential energy, {eq}\displaystyle E_{pot} = mgh {/eq} where {eq}\displaystyle g {/eq} is the gravitational acceleration and {eq}\displaystyle h {/eq} is the height. We can acquire the height at the top of the ramp through trigonomety, such that {eq}\displaystyle h = 0.12\ m\sin 34.74^\circ =0.068\ m {/eq}. We proceed to the solution.

{eq}\begin{align} \displaystyle \frac{1}{2}mv^2 &= mgh\\ v^2 &= 2gh\\ v&= \sqrt{2gh}\\ v&= \sqrt{2\cdot 9.81\ \rm{m/s^2}\cdot 0.068\ m }\\ v&\approx 1.2\ \rm{m/s} \end{align} {/eq} 