# Falling object

1. Jan 31, 2008

1. The problem statement, all variables and given/known data
a block 20% moe massive than yo uhangs from a rope. the other end of hte rpe goes over a massless frictionless pulley and dangles freely, with what acceleration must you climb th rope to keep the block from falling.

2. Relevant equations

possible w = mg
f = ma
p = mv

3. The attempt at a solution
mass of the body = 1 kg (easy to work with)
mass of block = 1.2 kg

the block falls w/ -g

if i want to keep the block from falling i haev to counter the block falling at

g * mass of block = 11.76 m/s^2 * kg

i feel like the answer is wrong because of units...

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2. Feb 1, 2008

bump =P

3. Feb 1, 2008

### chocokat

You have the (almost) correct answer, but I would suggest you change your process a bit.

You're looking for the acceleration of 'you' so that the block does not move. So, you're main goal is:

$$\Sigma F = ma = 0$$

We can use $$m_1$$ for the person, and $$m_2$$ for the block. And we know
$$m_2 = 1.2 m_1$$
and the weight of the block is $$m_2 g$$

The equation will look like:
$$m_1a + m_2g = 0$$
$$m_1a = -m_2g$$

Substituting for $$m_2$$ we get:
$$m_1a = -1.2 m_1 g$$
divide by $$m_1$$ to get
$$a = -1.2g$$
Then solve using -9.8 for g
$$a = 11.76 m/s^2$$

Even though it may seem more complicated, it is generally easier and cleaner just to leave unknown quantities as the variables, i.e. don't substitute some random amount such as the 1 you used for m.

4. Feb 1, 2008