At the low point in its swing, a pendulum bob with a mass of 0.2 kg has a velocity of 4 m/s What is the Kinetic at the low point? and Ignoring air resistance how high will the bob swing above the low point before reversing direction?
KE lowest point: 1/2 m v^2
How high? mgh= KE at lowest point, solve for h.
Well, well, let's swing into action and answer those questions for you!
First off, to find the kinetic energy at the low point, we can use the formula:
Kinetic Energy = 0.5 * mass * velocity^2
Plugging in the numbers you provided, we have:
Kinetic Energy = 0.5 * 0.2 kg * (4 m/s)^2
Calculating that out, we get:
Kinetic Energy = 0.5 * 0.2 kg * 16 m^2/s^2
Kinetic Energy = 1.6 J
So, the kinetic energy at the low point of the pendulum swing is 1.6 Joules. And now onto the height!
Considering there is no air resistance (which is often a real "drag"), the total mechanical energy of the pendulum is conserved. This means that the potential energy at the highest point will be equal to the initial kinetic energy at the lowest point.
Using the same formula, but this time solving for potential energy, we have:
Potential Energy = Kinetic Energy
0.5 * mass * velocity^2 = mass * g * height
Plugging in the numbers and rearranging the equation, we get:
4 m/s = 9.8 m/s^2 * height
height = 4 m/s / 9.8 m/s^2
height ≈ 0.41 m (rounded to two decimal places)
So, without air resistance slowing down our fun, the pendulum bob will swing approximately 0.41 meters above the low point before reversing direction.
Hope that swings with you, my friend!
To find the kinetic energy at the low point of a swinging pendulum bob, we can use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass of the bob (m) = 0.2 kg
Velocity of the bob (v) = 4 m/s
Step 1: Calculate the kinetic energy at the low point.
Kinetic Energy = (1/2) * mass * velocity^2
Kinetic Energy = (1/2) * 0.2 kg * (4 m/s)^2
Kinetic Energy = (1/2) * 0.2 kg * 16 m^2/s^2
Kinetic Energy = 1.6 J
Therefore, the kinetic energy at the low point of the pendulum bob is 1.6 Joules.
Now, to determine how high the bob will swing above the low point before reversing direction, we need to consider the conservation of energy. At the low point, all of the potential energy is converted to kinetic energy. As the bob swings upwards, the kinetic energy is converted back into potential energy. At the highest point, all of the kinetic energy is converted back into potential energy.
Since the kinetic energy at the highest point will be zero (because the bob comes to a momentary stop before reversing direction), we can set the initial kinetic energy equal to the final potential energy:
Initial Kinetic Energy = Final Potential Energy
Step 2: Solve for the height above the low point.
Kinetic Energy at the low point = Potential Energy at the highest point
(1/2) * mass * velocity^2 = mass * g * height
Substituting the given values:
(1/2) * 0.2 kg * (4 m/s)^2 = 0.2 kg * 9.8 m/s^2 * height
1.6 J = 1.96 N * height
Solving for height:
height = 1.6 J / (1.96 N)
height ≈ 0.816 m
Therefore, the bob will swing to a height of approximately 0.816 meters above the low point before reversing direction.
To find the kinetic energy at the low point of a pendulum, you can use the formula:
Kinetic energy = (1/2) * mass * velocity^2
In this case, the mass of the pendulum bob is 0.2 kg and the velocity at the low point is 4 m/s. Plugging these values into the formula:
Kinetic energy = (1/2) * 0.2 kg * (4 m/s)^2
= (1/2) * 0.2 kg * 16 m^2/s^2
= 1.6 J
Therefore, the kinetic energy at the low point of the pendulum is 1.6 Joules.
To calculate the height that the pendulum bob will swing above the low point before reversing direction, you can use the conservation of mechanical energy. At the highest point, the potential energy is equal to the initial kinetic energy.
Potential energy at the highest point = Kinetic energy at the low point
Using the formula for potential energy:
Potential energy = mass * gravity * height
Where:
mass = 0.2 kg (mass of the pendulum bob)
gravity = 9.8 m/s^2 (acceleration due to gravity)
height = the distance above the low point
Setting the potential energy equal to the kinetic energy:
mass * gravity * height = 1.6 J
Rearranging the equation to solve for the height:
height = 1.6 J / (mass * gravity)
= 1.6 J / (0.2 kg * 9.8 m/s^2)
≈ 0.816 m
Therefore, the pendulum bob will swing approximately 0.816 meters above the low point before reversing direction, assuming there is no air resistance.