To answer these questions, we need to understand the concepts of Gravitational Potential Energy (GPE), Kinetic Energy (KE), and Total Energy (TE).
Gravitational Potential Energy (GPE) is the energy possessed by an object due to its height and the force of gravity acting on it. The formula for calculating GPE is given by GPE = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height.
Kinetic Energy (KE) is the energy possessed by an object due to its motion. The formula for calculating KE is given by KE = 1/2 * m * v^2, where m is the mass and v is the velocity.
Total Energy (TE) is the sum of GPE and KE of an object. TE = GPE + KE.
Now, let's go through each question step by step.
a) Before his dad pushes him:
GPE: 50J (Given in the question)
KE: 0J (Since Timmy is sitting at rest)
TE: GPE + KE = 50J + 0J = 50J
b) Immediately after his dad pushed him:
GPE: 75J (Given in the question)
KE: 125J (Given in the question)
TE: GPE + KE = 75J + 125J = 200J
c) The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed from one form to another. In this case, Timmy's total energy changed because his dad applied a force to him, which resulted in the conversion of potential energy (GPE) to kinetic energy (KE).
d) At the top of Timmy's path:
In physics, we consider the top of the path as the maximum height attained. At this point, all of Timmy's initial GPE has been converted into KE.
GPE: 0J (Since he is at the maximum height)
KE: 200J (From the previous question)
TE: GPE + KE = 0J + 200J = 200J
e) As he swings back down through the bottom of his path:
At the bottom of the path, all of Timmy's initial KE has been converted back into GPE.
GPE: 200J (From the previous question)
KE: 0J (Since he is at the lowest point)
TE: GPE + KE = 200J + 0J = 200J
f) Timmy jumps off the swing just before he lands:
When Timmy jumps off the swing, his GPE is zero as he is at the ground level. His KE remains the same as it was just before he jumped.
GPE: 0J
KE: 200J (From the previous question)
TE: GPE + KE = 0J + 200J = 200J
g) After Timmy hits the ground:
Once Timmy hits the ground, both his GPE and KE become zero, as he comes to a complete stop.
GPE: 0J
KE: 0J
TE: GPE + KE = 0J + 0J = 0J
I hope this explanation helps you understand the concepts of GPE, KE, and TE and how they relate to Timmy's situation at different points in time.