Questions: An engineer is trying to determine the height from which she needs to release a 57 kg wrecking ball such that the wrecking ball will be traveling 11.1 m / s when it strikes the building at the position shown. Neglect drag. List the energy types at the initial and final time and whether work and loss (due to non-conservative forces) occur as well as the corresponding amounts of energy. initial: GPE J work? no work J loss? no loss 1 v final: GPE KE From what height above the ground does the engineer need to release the ball? x 6.3 unit Using g=9.8 m / s^2

An engineer is trying to determine the height from which she needs to release a 57 kg wrecking ball such that the wrecking ball will be traveling 11.1 m / s when it strikes the building at the position shown. Neglect drag.
List the energy types at the initial and final time and whether work and loss (due to non-conservative forces) occur as well as the corresponding amounts of energy.
initial:
GPE

J

work?
no work

J

loss?
no loss

1 v
final:
GPE KE

From what height above the ground does the engineer need to release the ball?
x 6.3

unit
Using g=9.8 m / s^2

Transcript text: An engineer is trying to determine the height from which she needs to release a 57 kg wrecking ball such that the wrecking ball will be traveling $11.1 \mathrm{~m} / \mathrm{s}$ when it strikes the building at the position shown. Neglect drag. List the energy types at the initial and final time and whether work and loss (due to non-conservative forces) occur as well as the corresponding amounts of energy. initial: $\square$ GPE \[ 1= \] $\square$ J $\square$ work? no work \[ = \] $\square$ J loss? no loss \[ 1= \] $\square$ $1 \quad v$ final: GPE \& KE $\square$ $\square$ From what height above the ground does the engineer need to release the ball? x 6.3 $\square$ unit Using $\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}$

Solution

Solution Steps

Step 1: Identify the energy types

Initially, the wrecking ball has potential energy due to its height above the reference level. As it falls, this potential energy is converted into kinetic energy. We can neglect air resistance (drag), so there is no energy loss. Since the only force acting on the wrecking ball is gravity, which is a conservative force, there is no work done.

Initial energy: Potential Energy (PE) Final energy: Kinetic Energy (KE)

Step 2: Set up the energy conservation equation

Since energy is conserved, the initial potential energy (PE) equals the final kinetic energy (KE):

PE = KE

mgh = (1/2)mv^2

where:

m = mass of the wrecking ball (57 kg)
g = acceleration due to gravity (9.81 m/s²)
h = height above the reference level where the ball needs to be released
v = velocity of the wrecking ball just before impact (11.1 m/s)

Step 3: Solve for the height (h)

We can simplify the equation by canceling out the mass (m) on both sides:

gh = (1/2)v^2

h = (v^2) / (2g)

h = (11.1 m/s)^2 / (2 * 9.81 m/s²)

h ≈ 6.29 m

This is the height above the reference level. Since the reference level is 5 meters above the ground, the total height above the ground is 6.29 m + 5 m = 11.29 m.

Final Answer

The engineer needs to release the ball from approximately 11.29 meters above the ground. Initial: PE = mgh Final: KE = (1/2)mv^2 Work: 0 J Loss: 0 J Height above ground: 11.29 m

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