At its highest point, the pendulum is 1.2m above the ground and as a gravitational potential energy of 62J. If the gravitational potential energy is 10J at its lowest point, what is the pendulum's kinectic energy at this point?
The difference in GPE from the highest point to the lowest pont=KE at bottom
the kinetic energy is zero, because when it is at the bottom it is not accelerating
To find the kinetic energy of the pendulum at its lowest point, we need to use the conservation of mechanical energy.
The mechanical energy of the pendulum is the sum of its potential energy (PE) and kinetic energy (KE) at any given point. According to the conservation of mechanical energy, the total mechanical energy remains constant throughout the swing of the pendulum, neglecting any energy losses due to air resistance or friction.
Given:
PE at highest point = 62J
PE at lowest point = 10J
Since the pendulum has its maximum potential energy at its highest point and minimum potential energy at its lowest point, the potential energy is converted into kinetic energy as it swings down.
Hence, we can use the conservation of mechanical energy to calculate the kinetic energy at the lowest point.
1. The total mechanical energy at the highest point (E1) is equal to the potential energy at that point:
E1 = PE1 = 62J
2. The total mechanical energy at the lowest point (E2) is equal to the sum of the potential energy and kinetic energy at that point:
E2 = PE2 + KE2 = 10J + KE2
Since the total mechanical energy is conserved, we have:
E1 = E2
Substituting the values into the equation, we get:
62J = 10J + KE2
To find KE2, we need to rearrange the equation:
KE2 = 62J - 10J
Simplifying the equation, we have:
KE2 = 52J
Therefore, the pendulum's kinetic energy at its lowest point is 52J.
To find the pendulum's kinetic energy at its lowest point, we need to apply the principle of conservation of mechanical energy, which states that the total mechanical energy of a system remains constant as long as only conservative forces, like gravity, are acting on it.
The mechanical energy of a pendulum consists of two components: gravitational potential energy (PE) and kinetic energy (KE). At any given point in the pendulum's motion, the sum of these two energies remains constant.
Given that the gravitational potential energy at the highest point is 62J and at the lowest point is 10J, we can determine the kinetic energy at the lowest point.
At the highest point:
Gravitational potential energy (PE_high) = 62J
At the lowest point:
Gravitational potential energy (PE_low) = 10J
Kinetic energy (KE_low) = ?
Since the total mechanical energy is conserved, we can express this relationship mathematically as:
PE_high + KE_high = PE_low + KE_low
Since the pendulum reaches its highest point momentarily, it is momentarily at rest. Therefore, its kinetic energy at the highest point is zero:
KE_high = 0
Using this information, we can rearrange the equation to solve for KE_low:
KE_low = PE_high + KE_high - PE_low
Substituting the given values:
KE_low = 62J + 0J - 10J
KE_low = 52J
Therefore, the pendulum's kinetic energy at its lowest point is 52J.