Finding theta in a ramp problem, given velocity, distance, accelration,and mu k,

[trollphysics]

Homework Statement

Velocity final is 8 m/s
velocity initial is 0m/s
acceleration is -1.6m/s2
distance is 20m
Mk is .2

Homework Equations

My teacher has given me sin(theta)=(square root) of 1-cos^2(theta)
and cos(theta) = x

The Attempt at a Solution

I'm a bit stuck, the part which I am up to is g^2 - g^2(x^2) = a^2 + 2(a(Mk(gx))) + (Mk(gx))^2

What are the steps after these to get the answer. I have checked with my teacher and he says that what I have so far is correct.

 

[tiny-tim]

hi trollphysics!

(have a theta: θ and a mu: µ and try using the X² and X₂ icons just above the Reply box )

… the part which I am up to is g^2 - g^2(x^2) = a^2 + 2(a(Mk(gx))) + (Mk(gx))^2

What are the steps after these to get the answer.

that's a quadratic equation in x, so just write it out clearly, and solve!

 

[trollphysics]

hi trollphysics!

(have a theta: θ and a mu: µ and try using the X² and X₂ icons just above the Reply box )


that's a quadratic equation in x, so just write it out clearly, and solve!

Hi tiny-tim,
my teacher had told me that this was a quadratic equation. But I don't really know how to set that up. All I have now are these variables. Any help would be appreciated and thanks for letting me know of the signs which the forum integrates.

 

[tiny-tim]

hi trollphysics!

my teacher had told me that this was a quadratic equation. But I don't really know how to set that up.

just write the equation out with all the x² terms together, then all the x terms together, then all the constants together, so that it's in the form ax² + bx + c …

what do you get? ​

 

[trollphysics]

hi trollphysics! just write the equation out with all the x² terms together, then all the x terms together, then all the constants together, so that it's in the form ax² + bx + c …

what do you get? ​

Would it come out to be:

a²+g²-g²x²+(µ(gx))² + 2(a(µ(gx))) = ?

Is this correct? or am I just doing it wrong?

 

[tiny-tim]

hi trollphysics!

(what happened to that µ i gave you? )

a²+g²-g²x²+(µ(gx))² + 2(a(µ(gx))) = ?

yes (except i think you got a sign wrong)

now tidy it up into the form ax² + bx + c = 0, and use the standard quadratic equation solution to solve it

 

[trollphysics]

hi trollphysics!

(what happened to that µ i gave you? )yes (except i think you got a sign wrong)

now tidy it up into the form ax² + bx + c = 0, and use the standard quadratic equation solution to solve it

Yes the mistake was in the moving of the left hand side...

Here is the proper way:
a²-g²x²+(µ(gx)²+2(a(µ(gx)))= 0

Now can I substitute in the variables or do I have to do something else?

 

[tiny-tim]

no, just plug and chug!

 

[trollphysics]

no, just plug and chug!

I'm sorry, but what?

 

[tiny-tim]

plug the numbers into the formula, and chug away like a steam engine