let’s say a marble that weighed 0.006 kg was on a 1 m tall ramp. It went down the ramp at a velocity of 4.4 (m/s) and went through a loop with a height of 0.25 m. The marbles ending velocity as it was at the end of the loop and end of the ramp was at a velocity of 1.7 (m/s). Calculate the amount of kinetic energy the marble has at the bottom of the drop
To calculate the amount of kinetic energy the marble has at the bottom of the drop, we need to find its initial and final kinetic energies.
Initial Kinetic Energy:
The marble starts at the top of the ramp, so its initial height is 1 m. The initial velocity is 0 m/s since it is not moving at the top of the ramp.
Therefore, the initial kinetic energy is given by:
KE_initial = 0.5 * mass * velocity_initial^2
= 0.5 * 0.006 kg * (0 m/s)^2
= 0 Joules
Final Kinetic Energy:
The marble reaches a velocity of 4.4 m/s at the bottom of the ramp. We will consider the height of the ramp and the loop together as the height from which the marble falls.
The total height from which the marble falls is 1 m + 0.25 m = 1.25 m.
The final velocity at the bottom of the drop is given as 1.7 m/s.
Therefore, the final kinetic energy is given by:
KE_final = 0.5 * mass * velocity_final^2
= 0.5 * 0.006 kg * (1.7 m/s)^2
= 0.00918 Joules
The amount of kinetic energy the marble has at the bottom of the drop is approximately 0.00918 Joules.