What Angle Does a Pendulum Form When It Stops?

[ThatDude]

Homework Statement

A 2 meter long pendulum passes its lowest point with a velocity of 4 m/s, then swings back up before temporarily coming to a stop. What angle does it then form with the vertical, if the air resistance is negligible?

2. The attempt at a solution

I know that the kinetic energy at the bottom will equal the potential energy at the top - that is when the pendulum comes to a temporary stop.

KE = PE

(1/2)(m)(16) = (m)(g)(h)

h = 0.82 meters

Now, I understand that this is the max height above the lowest point.

I can't figure out how to proceed from here. I don't have two components to find the angle.

 

[Panphobia]

Actually you do have two components, you have the height at the instance where it is coming to rest, and you have the radius of the pendulum.

 

[ThatDude]

Actually you do have two components, you have the height at the instance where it is coming to rest, and you have the radius of the pendulum.

I don't quite follow.

 

[mfb]

The vertical, dashed line is the radius as well.
What happens if you add a horizontal line at the height of your object?

 

[HalfLostAndSearching]

I would approach this problem by first identifying the key concepts and equations related to conservation of energy. In this case, we know that the total energy (KE + PE) of the pendulum remains constant throughout its motion, neglecting any external forces such as air resistance. Therefore, we can use the equation KE = PE to solve for the angle at which the pendulum comes to a temporary stop.

To do this, we can use the conservation of energy equation: KE = (1/2)mv^2 = PE = mgh, where m is the mass of the pendulum, v is the velocity at the lowest point, g is the acceleration due to gravity, h is the height at the top of the swing, and PE is the potential energy at the top of the swing.

We know the mass of the pendulum and the velocity at the lowest point, so we can solve for the height at the top of the swing. From there, we can use trigonometric functions to find the angle formed by the pendulum with the vertical.

It is also important to note that the angle formed by the pendulum at the top of the swing will be the same as the angle formed at the bottom of the swing, due to the symmetry of the pendulum's motion.

In conclusion, by applying the principles of conservation of energy and using the relevant equations, we can solve for the angle formed by the pendulum with the vertical at the top of its swing.