A. A particle is traveling without friction up and down hills and valleys. If its initial potential energy is 6 J and its initial kinetic energy is 78 J, what is its total energy, E?
E: J
B. If at a later point its potential energy is -14 J, what is its kinetic energy K at that point?
K: J
C. If at a still later point its kinetic energy is 61 J, what is its potential energy U at that point?
U: J
A. To find the total energy, E, of the particle, we need to add its potential energy (PE) and kinetic energy (KE) together.
Given:
Initial potential energy (PE) = 6 J
Initial kinetic energy (KE) = 78 J
Total energy (E) = PE + KE
Substituting the values:
E = 6 J + 78 J
Evaluating the sum:
E = 84 J
Therefore, the total energy (E) of the particle is 84 J.
B. To find the kinetic energy (K) of the particle at a later point when its potential energy is -14 J, we need to use the principle of conservation of energy.
The total energy (E) of the particle remains constant throughout its motion. At any point, the sum of its kinetic energy (K) and potential energy (U) will be equal to its total energy (E).
Given:
Potential energy (U) = -14 J
Using the conservation of energy principle:
E = K + U
Substituting the given values:
84 J = K + (-14 J)
Simplifying the expression:
84 J = K - 14 J
To find the value of K, we can rearrange the equation:
K = 84 J + 14 J
Evaluating the sum:
K = 98 J
Therefore, the kinetic energy (K) of the particle at that point is 98 J.
C. To find the potential energy (U) of the particle at a still later point when its kinetic energy is 61 J, we can use the conservation of energy principle.
Given:
Kinetic energy (K) = 61 J
Using the conservation of energy principle:
E = K + U
Substituting the given values:
84 J = 61 J + U
Simplifying the expression:
84 J = U + 61 J
To find the value of U, we can rearrange the equation:
U = 84 J - 61 J
Evaluating the subtraction:
U = 23 J
Therefore, the potential energy (U) of the particle at that point is 23 J.