Falling object

  • #1

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...
 

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Answers and Replies

  • #3
79
0
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:

[tex] \Sigma F = ma = 0 [/tex]

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

The equation will look like:
[tex]m_1a + m_2g = 0[/tex]
[tex]m_1a = -m_2g[/tex]

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

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
ah that makes sense how you got the units to end up correct, i like how you set it up, thanks!
 
  • #5
79
0
You're welcome!
 

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