How Much Work is Done by the Cake Batter on a Falling Worker?

[Jamest39]

Homework Statement

A 65-kg worker at a bakery loses his balance and falls 4.0 m before hitting the surface of a large vat of cake batter. He continues to travel downwards an additional 2.0 m before the cake batter finally brings him to rest. Calculate the work done on the worker by the cake batter.

Homework Equations

F = ma
ΔKE = Wnet
W = Fscosθ
PEgravity = mgh

The Attempt at a Solution

ΔKE = KEfinal - KEinitial = 0 - KEinitial ⇒ KEintitial = -(1/2)mv^2
PEgravity = mgh = (65 kg)(9.80 m/s^2)(4.0 m) = 2548 J

 

[gneill]

Consider that the worker is still falling (moving vertically) through the cake batter until he comes to rest.

 

[Jamest39]

Consider that the worker is still falling (moving vertically) through the cake batter until he comes to rest.

So,
F = ma = (65 kg)(9.80 m/s^2) = 637 N
W = Fscosθ = (637 N)(6.0 m)cos180° = -3822 J (6.0 as the displacement considering his whole movement?)

 

[gneill]

That will work. The basic premise is that the work falls a total of 6 m through the gravitational field and so gains energy Mgh from the change in gravitational potential energy. That total amount of energy is "lost" to the cake batter over distance that he travels through the batter.

 

[Jamest39]

That will work. The basic premise is that the work falls a total of 6 m through the gravitational field and so gains energy Mgh from the change in gravitational potential energy. That total amount of energy is "lost" to the cake batter over distance that he travels through the batter.

Was my answer right or do I still have to factor in the energy he lost while going through the batter?

 

[gneill]

Was my answer right or do I still have to factor in the energy he lost while going through the batter?

Your answer was fine. The energy lost to the batter is the energy gained from falling. That's why the worker comes to rest in the batter. That energy represents the work done by the batter. The only way you could improve your result would be to make sure that its stated to the correct number of significant figures.