A particle is traveling without friction up and down hills and valleys. If its initial potential energy is 85 J and its initial kinetic energy is 83 J, what is its total energy, E?
E:
Correct: Your answer is correct.
J
B. If at a later point its potential energy is 131 J, what is its kinetic energy K at that point?
K: J
C. If at a still later point its kinetic energy is 12 J, what is its potential energy U at that point?
U: J
B. To find the kinetic energy (K) at a later point, we can use the conservation of mechanical energy. The total mechanical energy (E) remains constant, so we can use the following equation:
E = K + U
Given that the potential energy (U) at the later point is 131 J, we can substitute the values into the equation:
85 J + 83 J = K + 131 J
Simplifying the equation:
168 J = K + 131 J
Subtracting 131 J from both sides:
168 J - 131 J = K
Therefore, the kinetic energy (K) at that later point is 37 J.
K: 37 J
C. To find the potential energy (U) at a still later point, we can again use the conservation of mechanical energy with the equation:
E = K + U
Given that the kinetic energy (K) at the still later point is 12 J, we can substitute the values into the equation:
85 J + 12 J = U + 12 J
Simplifying the equation:
97 J = U + 12 J
Subtracting 12 J from both sides:
97 J - 12 J = U
Therefore, the potential energy (U) at that still later point is 85 J.
U: 85 J
A. To find the total energy, E, of the particle, you need to add the initial potential energy (PE) and the initial kinetic energy (KE) together.
E = PE + KE
Given that the initial potential energy is 85 J and the initial kinetic energy is 83 J, you simply add them together:
E = 85 J + 83 J
E = 168 J
So, the total energy of the particle is 168 J.
B. To find the kinetic energy, K, at a later point when the potential energy is 131 J, you can apply the conservation of energy principle. In the absence of friction, the total energy remains constant.
E = PE + KE
Rearranging the equation, we can solve for the kinetic energy:
KE = E - PE
Substituting the given values, we have:
KE = 168 J - 131 J
KE = 37 J
Therefore, the kinetic energy at the later point is 37 J.
C. Using the same principle of conservation of energy, we can solve for the potential energy, U, when the kinetic energy is 12 J.
E = PE + KE
Again, rearranging the equation and substituting the given values:
PE = E - KE
PE = 168 J - 12 J
PE = 156 J
So, the potential energy at the still later point is 156 J.