At he lowest point in its swing, a 2.5 kilogram pendulum bob has 40 joules of kinetic energy. How high will it swing when it reaches the highest point in its swing?

40/2.5 x 9.8 = 1.63 joules

conservation of mech energy...

look at two spots, when the bob is at the lowest, and the highest...

KE (lowest) + KE (highest) = U (lowest ) + U (highest)

40J + 0J = 0J + mgh
40J = 2.5kg(9.81m/s^2)(height)
height = 1.6309m

To determine how high the pendulum will swing when it reaches the highest point, we can use the principle of conservation of energy. At the lowest point in its swing, all of the pendulum's kinetic energy is converted into potential energy.

We are given that the kinetic energy at the lowest point is 40 joules. Since kinetic energy is given by the equation KE = (1/2)mv^2, where KE is the kinetic energy, m is the mass, and v is the velocity, we can rearrange the equation to solve for velocity.

40 joules = (1/2)(2.5 kilograms)(v^2)

To find the velocity, we can divide both sides of the equation by (1/2)(2.5 kilograms).

40 joules / [(1/2)(2.5 kilograms)] = v^2

Simplifying further:

40 joules / 1.25 kilograms = v^2

v^2 = 32

Taking the square root of both sides, we find:

v = √32 ≈ 5.66 meters per second

Now, to determine the height at the highest point, we can use the conservation of energy. At the highest point, all of the initial kinetic energy is converted into potential energy. Potential energy is given by the equation PE = mgh, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height.

Therefore, we can write the equation as:

40 joules = (2.5 kilograms)(9.8 meters per second squared)(h)

Solving for h:

40 joules = 24.5 kilograms meters per second squared (h)

Dividing both sides by 24.5 kilograms meters per second squared:

h = 40 joules / 24.5 kilograms meters per second squared

Calculating:

h ≈ 1.63 meters

Therefore, the pendulum will swing upward to a height of approximately 1.63 meters when it reaches the highest point of its swing.