Maths problem(mechanics-friction)

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Maths problem(mechanics--friction)

A and B are points on the same line of greatest slope of a rough plane inclined at 30◦ to the horizontal.
A is higher up the plane than B and the distance AB is 2.25 m. A particle P, of mass mkg, is released
from rest at A and reaches B 1.5 s later. Find the coefficient of friction between P and the plane.

According to the book the answer is 0.346 and i cannot get the answer:

according to me: friction = mg sin 30

Reaction= mg c0s 30

using F = μ R

i replace but yet cannot get the right answer...please try to work it out i think my method is wrong..?????
 

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A and B are points on the same line of greatest slope of a rough plane inclined at 30◦ to the horizontal.
A is higher up the plane than B and the distance AB is 2.25 m. A particle P, of mass mkg, is released
from rest at A and reaches B 1.5 s later. Find the coefficient of friction between P and the plane.

According to the book the answer is 0.346 and i cannot get the answer:

according to me: friction = mg sin 30

Reaction= mg c0s 30

using F = μ R

i replace but yet cannot get the right answer...please try to work it out i think my method is wrong..?????


Your equation for friction is totally wrong, what you have there is the equation of the force of gravity on the particle acting down the plane. However your two next equations are correct. Try to make an overall force equation. I'd really recommend drawing a diagram and labelling the forces.

Other things you'll have to consider;

Equations of motion, (SUVAT), you have the distance between A & B, and the time second to pass from one to the other. What can you work out from those 2 pieces of information that would be helpful here? (we're considering forces....). Also bear in mind it starts from rest so u = 0.
 

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