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.
Shoot, your kinetic energy amount ever been more than the potential energy at the beginning? why or why not?
To calculate the amount of kinetic energy the marble has at the bottom of the drop, we can use the equation:
Kinetic Energy = 0.5 * mass * velocity^2
Given:
Mass of marble (m) = 0.006 kg
Velocity at the bottom (v) = 1.7 m/s
Kinetic Energy = 0.5 * 0.006 kg * (1.7 m/s)^2
= 0.01026 J
Therefore, the amount of kinetic energy the marble has at the bottom of the drop is 0.01026 Joules.
Now, let's address the second part of your question regarding the comparison of kinetic energy and potential energy.
The potential energy at the beginning of the ramp can be calculated using the formula:
Potential Energy = mass * acceleration due to gravity * height
Given:
Mass of marble (m) = 0.006 kg
Height of the ramp (h) = 1 m
Acceleration due to gravity (g) = 9.8 m/s^2
Potential Energy = 0.006 kg * 9.8 m/s^2 * 1 m
= 0.0588 J
Therefore, at the beginning of the ramp, the marble has a potential energy of 0.0588 Joules.
In this particular scenario, the kinetic energy of the marble at the bottom of the drop (0.01026 J) is indeed less than the potential energy at the beginning (0.0588 J). This is because some of the potential energy is converted into other forms of energy (like kinetic energy) during the marble's descent down the ramp and through the loop. The conservation of energy principle states that energy can neither be created nor destroyed, only transferred or transformed from one form to another.