A frictionless pendulum of length 3 m swings
with an amplitude of 10◦. At its maximum
displacement, the potential energy of the pendulum is 10 J.
What is the kinetic energy of the pendulum
when its potential energy is 5 J?
1. K = 10 J
2. K = 3.3 J
3. K = 6.7 J
4. K = 15 J
5. K = 5 J
5. K =5 J
since the only force acting on it is gravity, it's a conservative force. That means the energy is only transferred from U to KE and never lost.
We use the formula:
E= U + KE
At its max displacement, KE=0 and E must equal U. It says that at its max displacement U=10J so at that point E also equals 10J.
So if E=10 and U=5, KE=?
E= U+KE
10=5+KE
KE=5J
5 J
Well, well, well, we've got a swinging pendulum here! Let's see if I can crack a few jokes to help you with your question.
First, remember that the total mechanical energy of the pendulum remains constant throughout its motion. That means the sum of potential energy and kinetic energy is always the same.
So, if the potential energy is 10 J at the maximum displacement and then drops to 5 J, we just need to find the difference between those two energies to find the kinetic energy!
Now, let the comedy begin! 🎭
If the potential energy is walking down the stairs, the kinetic energy is like zooming downhill on a skateboard with a banana peel under your foot! It's all about that fast, funny, and furious energy!
So, the difference in potential energy is 10 J - 5 J = 5 J of potential energy converted to kinetic energy!
Drum roll, please... 🥁
Therefore, the kinetic energy of the pendulum when the potential energy is 5 J is 5 J! So the answer is option 5. K = 5 J.
Hope that helps, and keep swinging through those physics problems like a clown on a trapeze! 🤡
To determine the kinetic energy of the pendulum when its potential energy is 5 J, we can make use of the conservation of mechanical energy for a pendulum. In a frictionless system, the total mechanical energy remains constant.
The total mechanical energy of the pendulum is given by the sum of its kinetic energy (K) and potential energy (U):
E = K + U
Given that the potential energy at maximum displacement is 10 J, and we want to find the kinetic energy when the potential energy is 5 J, we can set up the following equation:
10 J = K + 5 J
Subtracting 5 J from both sides of the equation, we get:
5 J = K
Therefore, the kinetic energy of the pendulum when its potential energy is 5 J is 5 J.
So, the correct answer is option 5: K = 5 J.
To find the kinetic energy of the pendulum when its potential energy is 5 J, we can use the principle of conservation of mechanical energy. The total mechanical energy of the pendulum, which is the sum of its potential energy and kinetic energy, remains constant throughout its motion.
Given that the potential energy of the pendulum at maximum displacement is 10 J, we know that the total mechanical energy is 10 J at that point.
At maximum displacement, the potential energy is at its maximum, and therefore the kinetic energy is at its minimum. This means that the kinetic energy is zero at maximum displacement.
As the pendulum swings away from its maximum displacement, the potential energy decreases while the kinetic energy increases. When the potential energy reaches 5 J, we can assume that the kinetic energy has increased to a non-zero value.
Since the total mechanical energy is constant, we can calculate the kinetic energy when the potential energy is 5 J by subtracting the potential energy from the total mechanical energy.
Kinetic energy = Total mechanical energy - Potential energy
Kinetic energy = 10 J - 5 J
Kinetic energy = 5 J
Therefore, the kinetic energy of the pendulum when its potential energy is 5 J is 5 J.
The correct answer is option 5: K = 5 J.