Crate on a slope - Angles and Tension


by mybrohshi5
Tags: angles, crate, slope, tension
mybrohshi5
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#1
Feb14-10, 11:18 AM
P: 365
1. The problem statement, all variables and given/known data

A large empty crate, with its lid in place, has a 9.50 kg mass hanging from a string attached to the center of the lid. If the crate were sitting (at rest) on a flat surface, the string would simply hang straight down such that the mass would not be touching the floor of the crate.

The crate is now pushed up a frictionless 10.0 degree slope with an acceleration of 2.25 m/s^2. During the push, what angle does the string make with the lid of the crate? Hint: you will need to solve two equations in two unknowns.

2. Relevant equations

f=ma
newton's 2nd law

3. The attempt at a solution

I found the force required to push it up the ramp

f= 9.8(9.5)sin10 = 16.2N

Not sure if i even need that but i did it anyways.

so i really have no idea what 2 equations i need to get in order to solve the angle of the string?

can anyone help me on this please.

thank you
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aim1732
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#2
Feb14-10, 01:19 PM
P: 431
What about a free body diagram with the pseudo forces included?
tiny-tim
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#3
Feb14-10, 01:56 PM
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Hi mybrohshi5!

The acceleration of the mass will be the same as that of the crate (and in the same direction). And there are two forces on the mass.

So use good ol' Newton's second law on the mass
what do you get?

mybrohshi5
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#4
Feb14-10, 02:16 PM
P: 365

Crate on a slope - Angles and Tension


well the two forces would be the force due to gravity (its weight) and the normal force is that correct?

im a little confused about what i need to find from what you just stated above.

thank you for any further explanations
tiny-tim
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#5
Feb14-10, 02:22 PM
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Hi mybrohshi5!
Quote Quote by mybrohshi5 View Post
well the two forces would be the force due to gravity (its weight) and the normal force is that correct?
Normal force? Normal to what? It's not touching anything.

Add the two forces (one is unknown, so just give it a letter), and use F = ma.
mybrohshi5
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#6
Feb14-10, 02:27 PM
P: 365
i thought there was a normal force but i guess cause it frictionless there is not a normal force?

im sorry im so lost right now about adding the two forces (one is unknown) and use f = ma
tiny-tim
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Feb14-10, 02:34 PM
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Quote Quote by mybrohshi5 View Post
i thought there was a normal force but i guess cause it frictionless there is not a normal force?
Are you talking about the crate?

I'm asking about the mass hanging, inside it.

What is the Ftotal = ma equation for the mass?
mybrohshi5
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#8
Feb14-10, 02:43 PM
P: 365
sorry i was reading the question completely wrong

for some reason i am having a really hard time wrapping my head around what is going on still though and how to find these equations :(

the mass will have two forces on it correct.

one force will be the weight

and the other force will be the force parallel to the ramp just in the opposite direction?

im just really confused.... do i need to include tension in these two equations that i am trying to find?
tiny-tim
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#9
Feb14-10, 02:48 PM
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Quote Quote by mybrohshi5 View Post
im just really confused.... do i need to include tension in these two equations that i am trying to find?
You are confused, aren't you?

Yes, the tension is the only other force on the mass.

ok, so solve the vector equation: mg + T = ma.
(and get some sleep! )
mybrohshi5
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#10
Feb14-10, 02:52 PM
P: 365
im trying to figure out how this helps me solve the angle i need to find though....?
mybrohshi5
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#11
Feb14-10, 02:54 PM
P: 365
are these the two equations i need:

mgsin(10) + T = ma

T - mgsin(theta) = ma
tiny-tim
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Feb14-10, 04:19 PM
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Quote Quote by mybrohshi5 View Post
are these the two equations i need:

mgsin(10) + T = ma

T - mgsin(theta) = ma
uhh? what are they supposed to be?
mybrohshi5
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#13
Feb14-10, 04:23 PM
P: 365
goodness i am not exactly sure. i am so confused on how to get two equations for this.

ok, so solve the vector equation: mg + T = ma.

when you said this should i solve it for the tension?
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Feb14-10, 04:30 PM
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Quote Quote by mybrohshi5 View Post
goodness i am not exactly sure. i am so confused on how to get two equations for this.

ok, so solve the vector equation: mg + T = ma.

when you said this should i solve it for the tension?
Yes. T has magnitude and direction (and the question only asks you for the direction).

You will need to take components in a suitable direction, of both a and the forces.

You have a choice of three pairs of components:

horizontal/vertical

slope/normal

string/perpendicular-to-string

which do you think will be quickest?
mybrohshi5
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#15
Feb14-10, 04:39 PM
P: 365
my guess would be string/perpendicular to the string?

but maybe would it be slope/normal because the angle i am trying to find has to deal with the slope and the crate....
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Feb14-10, 04:54 PM
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Quote Quote by mybrohshi5 View Post
my guess would be string/perpendicular to the string?
Yes, that will be quicker because you don't want to find the magnitude of T, so you can avoid it by using components perpendicular to it.
mybrohshi5
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#17
Feb14-10, 05:06 PM
P: 365
so in the equation mg + T = ma

do i replace T with the components perpendicular to the string?

gosh i feel so stupid right now. i cannot even begin to explain how confused i am about this whole problem :(

am i just making it much more difficult than it actually is because thats what i feel i am doing :(
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#18
Feb14-10, 05:14 PM
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Quote Quote by mybrohshi5 View Post
so in the equation mg + T = ma

do i replace T with the components perpendicular to the string?
"replace"?

You use the components perpendicular to the string for the whole of mg + T = ma.


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