A 1250 KG wrecking ball is lifted to a height of 12.7 m above its resting point . When the wrecking ball is released, its swings toward an abandoned building and makes an indentation of 43.7 cm in the wall.

A) What is the potential energy of the wrecking ball at a height of 12.7 m?

B) What is its kinetic energy at the time of striking the wall?

C) If the wrecking ball transfers all of its kinetic energy to the wall, how much force does the wrecking ball apply to the wall?

D) Why should a wrecking ball strike a wall at the lowest point in its swing?

A) To find the potential energy of the wrecking ball at a height of 12.7 m, we can use the formula for gravitational potential energy:

Potential energy = mass * gravity * height

The mass of the wrecking ball is given as 1250 kg, and the height is 12.7 m. The acceleration due to gravity is approximately 9.8 m/s^2.

Potential energy = 1250 kg * 9.8 m/s^2 * 12.7 m = 156925 J

So, the potential energy of the wrecking ball at a height of 12.7 m is 156925 J.

B) To find the kinetic energy of the wrecking ball at the time of striking the wall, we need to know its speed at that point. Since the wrecking ball swings from a height and moves towards the wall, it will have converted all its potential energy into kinetic energy at the point of impact. So, we can use the principle of conservation of energy to find the kinetic energy.

Kinetic energy = Potential energy at the height - Potential energy at the point of impact

Potential energy at the height (as calculated in part A) = 156925 J
Potential energy at the point of impact = 0 J (since it has been completely converted into kinetic energy)

Therefore, the kinetic energy of the wrecking ball at the time of striking the wall is 156925 J.

C) If the wrecking ball transfers all of its kinetic energy to the wall, we can calculate the force applied to the wall using the equation:

Force = change in momentum / time

Since the wrecking ball comes to a stop after striking the wall, its momentum changes from a positive value to zero. The change in momentum is equal to the momentum before the collision.

Momentum = mass * velocity

The mass of the wrecking ball is given as 1250 kg, and to find the velocity, we can use the equation:

Potential energy at the height = Kinetic energy at the point of impact

- mgh = 1/2 * mv^2

Here, h is the height and v is the velocity.
Substituting the given values:

- 1250 kg * 9.8 m/s^2 * 12.7 m = 1/2 * 1250 kg * v^2

Simplifying the equation, we find:

v = sqrt((2 * 1250 kg * 9.8 m/s^2 * 12.7 m) / 1250 kg) = sqrt(2 * 9.8 m/s^2 * 12.7 m) ≈ 15.14 m/s

Now, substituting the values into the force equation:

Force = 1250 kg * 15.14 m/s / time

Since we don't have the time of collision provided in the question, we cannot calculate the exact force applied to the wall without further information.

D) A wrecking ball should strike a wall at the lowest point in its swing because, at the lowest point, it has the maximum potential energy and therefore the maximum kinetic energy. This allows for the most effective transfer of energy to the target, such as the wall. Additionally, striking at the lowest point ensures that the wrecking ball does not swing back and potentially cause damage to other objects or people.