A mechanics question about resolving forces! Watch

Jian17
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Hello guys, I´ve been struggling for a while with this mechanics question .
It´s about resolving forces check it out:

A, B and C are three points on a line of greatest slope of a smooth plane inclined at an angle of θ◦ to the horizontal. A is higher than B and B is higher than C, and the distances AB and BC are 1.76 m and 2.16 m respectively. A particle slides down the plane with constant acceleration a m s−2.

The speed of the particle at A is u m s−1 (see diagram). The particle takes 0.8 s to travel from A to B and takes 1.4 s to travel from A to C.

Find

(i) the values of u and a,
(ii) the value of θ.

Diagram:
https://gyazo.com/b531262b9ee9d4574fc0164b409407a3

The answers are: u = 1.4 , a = 2 and the angle is equal to 11.5

I´ve managed to work out the values of u and a, but I would appreciate if you could find those too because i got for a = 1.6666666...

Thanks!!!
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RDKGames
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(Original post by Jian17)
...
The given official answers are indeed correct.
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RogerOxon
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(Original post by Jian17)
Hello guys, I´ve been struggling for a while with this mechanics question .
It´s about resolving forces check it out:

A, B and C are three points on a line of greatest slope of a smooth plane inclined at an angle of θ◦ to the horizontal. A is higher than B and B is higher than C, and the distances AB and BC are 1.76 m and 2.16 m respectively. A particle slides down the plane with constant acceleration a m s−2.

The speed of the particle at A is u m s−1 (see diagram). The particle takes 0.8 s to travel from A to B and takes 1.4 s to travel from A to C.

Find

(i) the values of u and a,
(ii) the value of θ.

Diagram:
https://gyazo.com/b531262b9ee9d4574fc0164b409407a3

The answers are: u = 1.4 , a = 2 and the angle is equal to 11.5

I´ve managed to work out the values of u and a, but I would appreciate if you could find those too because i got for a = 1.6666666...
Could you post your working? We can then highlight any mistakes.
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Jian17
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After revising my working out, i realized the error i made so i found the answers for a and u, but i still can´t do section b from this question which is finding the angle.

Here´s how i did section a:
Ok, for the first part i did silmultaneous equations from distances AB and AC

s = ut + 0.5at^2

1.76 = 0.8u + 0.5a*0.8^2 3.92 = 1.4u + 0.5a*1.4^2

0.8u = 1.76 - 0.32a 1.4u = 3.92 - 0.98a
(Make "u" the same)

1.4u = 3.08 - 0.56a 1.4u = 3.92 - 0.98a

3.08 - 0.56a = 3.92 - 0.98a

0.42a = 0.84

a= 2 ms-2

substitute to find u: 1.4u = 3.08 - 0.56(2)
u = 1.4 ms-1

--------------------------------------------------------

Now, how do I find the value of θ ??
Diagram is above
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the bear
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the acceleration downhill on a smooth slope is always gsinθ
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Jian17
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Thanks! but could you tell me why is it always gsinθ?
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simon0
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(Original post by Jian17)
Thanks! but could you tell me why is it always gsinθ?
This is by resolving the forces down the slope by using your diagram (in your first post).

In your diagram, you are missing the weight of the object (as well as the reaction by the plane on the object but this does not matter here). By adding the effect of the weight we can then resolve.
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RDKGames
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(Original post by Jian17)
Thanks! but could you tell me why is it always gsinθ?
Because of this simple diagram for acceleration:

Spoiler:
Show

Name:  acce.PNG
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Size:  9.0 KB


The blue line is clearly your object's direction of acceleration, but it is merely a component of the overall force that is gravity with g
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