Question

A ball with a mass of 13g is resealed from rest through a ramp. The ramp has a length of 1 meter and it is inclined at an angle of 45 degrees to the horizontal. If friction is neglected, what is speed of the ball when it reaches the bottom of the ramp

Answer 1

Velocity =3.72 [m/s]

Step-by-step explanation:

We can solve this problem using the principle of energy conservation

If we take the reference point at the bottom of the ramp where the potential energy will be 0 and the top of the ramp where the mechanical energy is maximum.

In the attached image we have a detailed sketch with the conditions of the ball moving down without friction.

Then using the properties of a rectangle triangle we have:

`sin(\alpha )= (h)/(1) \\h=sin (45)*1\\h = 0.707[m]\\where\\h= elevation of the ball with respect to the reference point`

the potential energy will be:

`Ep=m*g*h\\where:\\m = mass of the ball = 0.013[kg]\\g=gravity = 9.81 [m/s^s]\\h = 0.707 [m]`

`Ep= 0.013 [kg]*9.81 [m/s^s]*0.707[m]\\Ep=0.090[J]\\`

This energy is transformed to kinetic energy

`Ek=(1)/(2)*m*v^(2)  \\where\\v=velocity of the ball [m/s]\\`

`v=\sqrt{((2*Ek)/(m) )} \\Ek=Ep\\v=\sqrt{((2*0.09)/(0.013) )} \\\\v=3.72[m/s]`