# Work-Energy Kinematics HW Help

1. May 29, 2012

### Parzival

1. The problem statement, all variables and given/known data
At a carnival, you can try to ring a bell by striking a target with a 9.00 kg hammer. In response, a 0.400 kg metal piece is sent upward toward the bell, which is 5.00 m above. Suppose that 25.0% of the hammer's kinetic energy is used to do the work of sending the metal piece upward. How fast must the hammer be moving when it strikes the target so that the bell just barely rings?

2. Relevant equations

W = final mechanical energy - initial mechanical energy

1/2m*final velocity^2 + mg*finalheight = 1/2m*initial velocity^2 + mg*initial height

Conservation of mechanical energy

3. The attempt at a solution
I tried setting up an equation using the second given equation, but unfortunately there are too many variables.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. May 29, 2012

### rock.freak667

Start simple, how much energy will it take to raise 0.4 kg mass to a height of 5 m?

What is the expression for KE?

3. May 29, 2012

### Parzival

KE = 1/2mv^2;

or KE = mg(hf - h0)

4. May 29, 2012

### rock.freak667

Right but they said that 25% of the hammer's KE is used to do the work, so how should you incorporate this into the equation?

5. May 30, 2012

### Parzival

KE = 1/8mv^2

or KE = 1/4mg(hf-h0)

6. May 30, 2012

### rock.freak667

Correct.

So now you have 1/8mv2=Mg(hf-h0)

You know m, M,g, hf and h0, solve for v.

7. May 30, 2012

### Parzival

So: v^2 = 8mMg(hf - h0)

v = sqrt(8mMg(hf-h0))

but what is h0? Do I assume it is 0 m?

And there are two masses: the 0.400 kg one and the 9.00 kg one.

8. May 30, 2012

### rock.freak667

Recheck your algebra on this one, you will need to divide by something.

Yes it is zero.

Right, which mass has the kinetic energy? Which mass will have the potential energy gain?

9. May 30, 2012

### Parzival

Sorry, I failed miserably. The equation is

sqrt(8Mg(hf-h0)/ m)

Let me guess. Plug in the numbers; then, multiply this by four to get the original KE, and then solve for the final velocity.

10. May 30, 2012

### rock.freak667

Well you already have the formula for the final velocity v.

$$v = \sqrt{\frac{8Mg(h_f -h_0)}{m}}$$

So just input all the numbers.

11. May 30, 2012

### Parzival

Sorry, I forget. What does capital M represent? I know lowercase m represents the mass, right?

12. May 30, 2012

### rock.freak667

Both are mass. One is just the mass of the hammer and the other is the mass of the piece of metal.