Acceleration Needed to Keep Block From Falling

[nightshade123]

Homework Statement

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.

Homework Equations

possible w = mg
f = ma
p = mv

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...

 

[nightshade123]

bump =P

 

[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.

 

[nightshade123]

ah that makes sense how you got the units to end up correct, i like how you set it up, thanks!

 

[chocokat]

You're welcome!