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We will now use energy considerations to find the speed of a falling object at impact. Artiom is on the roof replacing some shingles when his 0.55 kg hammer slips out of his hands. The hammer falls 3.67 m to the ground. Neglecting air resistance, the total mechanical energy of the system will remain the same. The sum of the kinetic energy and the gravitational potential energy possessed by the hammer 3.67 m above the ground is equal to the sum of the kinetic energy and the gravitational potential energy of the hammer as it falls. Upon impact, all of the energy is in a kinetic form. The following equation can be used to represent the relationship:
GPE + KE (top) = GPE + KE (at impact)

⦁ A Notice that the mass of the hammer "m" is shown on both sides of the equation. According to the math rules we have learned, what does this mean?

⦁ B Manipulate the equation (rearrange the variables) to solve for v. (Remember that manipulating an equation does not involve numbers and substitutions. You just rearrange the equation. v = ?)

⦁ C Use your equation from part B to find the speed with which the hammer struck the ground.

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leena leena · Answer 1 · 2022-01-15T19:36:15+01:00

Hi there!

Recall that:

GPE = mgh

KE = 1/2mv²

At the TOP of an object's trajectory, the GPE is at a maximum. There is NO kinetic energy at this moment.

At the bottom of the fall, the KINETIC energy is at a maximum while the GPE is a minimum (assuming the ground to be the zero-line.)

We can write this out:

GPE = KE

mgh = 1/2mv²

A.

There is an 'm' on both sides, so you can divide both sides by 'm':

(mgh)/m = 1/2mv²/m

gh = 1/2v²

B.

Solve for v.

gh = 1/2v²

Multiply both sides by 2:

2gh = v²

Take the square root:

v = √2gh

C.

We can use the equation:

v = √2gh

g = acceleration due to gravity (9.8 m/s²)

h = length of fall (3.67 m)

v = velocity (m/s)

Plug in the knowns:

v = √2(9.8)(3.67) = 8.48 m/s