A 0.09 kg marble sits at rest on the top of a sloping, frictionless track. a. If the slope has a height of 1.5 m, calculate the velocity of the marble at the bottom of
the slope.

Explanation:

Notice that nothing but the mass and height are given, and the mass is not really necessary. It will cancel when we do the problem.

So the potential energy at the top equals the Kinetic energy at the bottom.

PE_top = Ke_bottom

mgh = 1/2 m v^2          Divide by m

mgh/m =1/2 mv^2/m

gh = 1/2 v^2                  Multiply both sides by 2

2gh = v^2                    

Givens

g = 9.81

h = 1.5

Solution

2*9.81 * 1.5 = v^2

29.43 = v^2

v = sqrt(29.43)

v = 5.425

resonant frequency