Calculate Inertia: What is the Mass of the Crate?

[emily081715]

Homework Statement

A mysterious crate has shown up at your place of work, Firecracker Company, and you are told to measure its inertia. It is too heavy to lift, but it rolls smoothly on casters. Getting an inspiration, you lightly tape a 0.60-kg iron block to the side of the crate, slide a firecracker between the crate and the block, and light the fuse. When the firecracker explodes, the block goes one way and the crate rolls the other way. You measure the crate's speed to be 0.064 m/s by timing how long it takes to cross floor tiles. You look up the specifications of the firecracker and find that it releases 9 J of energy. That's all you need, and you quickly calculate the inertia of the crate.

Homework Equations

p=mv
k=1/2mv²

The Attempt at a Solution

i know the inertia is referring to the mass of the crate. will i need to use the chang in kinetic energy equation to solve for mass?

 

[BvU]

Nice story. Good thing the crate wasn't full of firecrackers or pure gunpowder (not unthinkable in such a company...).
Teacher must have had a good time composing it. He doesn't tell you how much of the 9 J is converted to kinetic energy, but I guess you should assume 100%. So the crate comes away undented and undamaged.

Yess, the exercise wants the mass of the crate. Aside from your two equations you'll need a bit more: energy conservation, momentum conservation, to name some. Start your attempt at solution and post when stuck ...

 

[I like Serena]

Homework Statement

A mysterious crate has shown up at your place of work, Firecracker Company, and you are told to measure its inertia. It is too heavy to lift, but it rolls smoothly on casters. Getting an inspiration, you lightly tape a 0.60-kg iron block to the side of the crate, slide a firecracker between the crate and the block, and light the fuse. When the firecracker explodes, the block goes one way and the crate rolls the other way. You measure the crate's speed to be 0.064 m/s by timing how long it takes to cross floor tiles. You look up the specifications of the firecracker and find that it releases 9 J of energy. That's all you need, and you quickly calculate the inertia of the crate.

Homework Equations

p=mv
k=1/2mv²

The Attempt at a Solution

i know the inertia is referring to the mass of the crate. will i need to use the chang in kinetic energy equation to solve for mass?

Hey Emily! ;)

We have 2 unknowns: the mass of the mysterious crate, and the speed of the firecracker after the explosion.
To find them we need 2 equations.
Can we set up the equations for conservation of momentum and conservation of energy?

 

[emily081715]

Hey Emily! ;)

We have 2 unknowns: the mass of the mysterious crate, and the speed of the firecracker after the explosion.
To find them we need 2 equations.
Can we set up the equations for conservation of momentum and conservation of energy?

m_c(v_ci-v_cf)=m_b(v_bf-v_bi)
v_ci-v_bi=v_bf-v_cf

would i be using theses? for the second equation i divided out mass and the 1/2 and rearranged a bit

 

[I like Serena]

m_c(v_ci-v_cf)=m_b(v_bf-v_bi)
v_ci-v_bi=v_bf-v_cf

would i be using theses? for the second equation i divided out mass and the 1/2 and rearranged a bit

The first, yes, and we already know that the initial velocities are zero.
The second equation doesn't look right. I doesn't seem to be related to energy.
Oh, and it's too early to divide out mass or the 1/2. First we need to relate it to the given 9 J of energy.

He doesn't tell you how much of the 9 J is converted to kinetic energy, but I guess you should assume 100%. So the crate comes away undented and undamaged.

I don't see how it could ever be 100%. ;)
Instead I'm assuming we're only given the part of the energy that is converted to mechanical energy. That is, I think the word "mechanical" was accidentally omitted in the problem statement.

 

[BvU]

for the second equation i divided out mass

That is not very wise: the mass of the crate is quite different from the mass of the block.