How Fast Must the Hammer Move to Ring the Bell at the Carnival?

[Parzival]

Homework Statement

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?

Homework 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

The Attempt at a Solution

I tried setting up an equation using the second given equation, but unfortunately there are too many variables.

 

[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?

 

[Parzival]

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?

KE = 1/2mv^2;

or KE = mg(hf - h0)

 

[rock.freak667]

KE = 1/2mv^2;

or KE = mg(hf - h0)

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?

 

[Parzival]

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?

KE = 1/8mv^2

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

 

[rock.freak667]

KE = 1/8mv^2

Correct.

So now you have 1/8mv²=Mg(h_f-h₀)

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

 

[Parzival]

Correct.

So now you have 1/8mv²=Mg(h_f-h₀)

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

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.

 

[rock.freak667]

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

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

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

Yes it is zero.

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

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

 

[Parzival]

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?

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.

 

[rock.freak667]

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.

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.

 

[Parzival]

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

 

[rock.freak667]

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

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