Held Art

can somebody help me this problem pleaseeeeeeee?

object of masses m1=3.50kg amd m2=9.50kg are connected by a light string that passes over frictionless pulley . the object m1 is held art rest on the floor and m2 at rest on a fixed inclined of teta 43.0 degress. the objects are then released fron rest and m2 slides 1.00m down the incline in 4.25s
a)determine the magnitude of acceleration of each object
b)the magnitude of the tension in the string
c)the coeficient of kinetic friction between m2 and the incline.

please help me to at least start thanks

The solution depends on how the string runs from the pulley to m1 and m2. You don't give this data which is, I suspect, (together with your frightful grammar & spelling) what's putting folk off trying to help you. Nobody likes to answer an unclear question. However, your appeal is very passionate, so I will at least respond. Let's hope it's what you need!

I shall assume that the pulley is vertically above mass m1 and that the string runs parallel to the slope from the pulley to mass m2. Does that correspond to your specification? If not, the answer will be wrong!!

Let the (upward) acceleration in m/s^2 of mass m1 be "a". This is automatically equal to the acceleration of m2 down the slope, because they are connected by the string

We can write:

Tension in string = (9.81 + a).m1 Newtons. .................... (1)

Summing the forces (upward + downward -) acting on m2 along the slope we get:

(9.81 + a)3.5 + Cf.(9.5 x 9.81).cos43 + 9.5a - (9.5 x 9.81).sin43 ..................(2)

where the 4 terms correspond to:

1. tension in string
2. friction (Cf = friction coefficient) - acting up the slope
3. reaction force to acceleration of m2 - (down the slope)
4. weight of m2 (component down the slope)

Now the distance travelled by m2 down the incline = s =1/2 a.t^2 where s= distance, t = time

so a = 2.s/(t^2) = 0.1107m/s^2

Now we can substitute this value of a in equation (2) and solve it for Cf
But first the tension in the string drops out of equation (1) as 3.5 x (9.81 + 0.1107) = 34.722N

Finally Cf = {9.81(9.5sin43 -3.5)} - (13 x 0.1107)}/(9.81 x 9.5 x cos43) = 0.407

So your answers are:

a) m1 and m2 accelerate by the same amount (0.1107m/s^2), m1 upwards, m2 down the slope.
b) tension in string is 34.722 N
c) coefficient of friction = 0.407

- all assuming my initial assumptions are correct and I made no mistakes

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