Question

Hello
this question is for my physics homework
"display knowledge of static and kinetic coefficients of friction, and calculate one of them to solve a problem"

Please answer it fast

thank you

Answer 1

Frictional force is a non conservative force which always acts in direction apposite to that of the motion of the object.

For example; Air friction, the friction between cart and ramp.

Now the frictioanl force is of two types:

static and kinetic friction, given by

Fs = us N and Fk = uk N

where us and uk are the coefficient of static and kinetic friction respectively.

Static friction coefficient is used when, you try to push an obejct and the object des not move, in other words the frictional force is greater than the applied force and hence the object does not move. In order for this object to move a minimum force equal to the static frictional force is required.

Kinetic friction coefficient is used when you try to push the object harder than earlier and it started to slide, and we need to keep applying the force so that it remain sliding. This is kinetic frictional force. Mostly its lesser than the statis frictional coefficient in magnitude.

Problem:

Let us consider an object moving on the ramp of angle theta to the horizontal.

the component of gravity acting is:

Fg = mg sin(theta) (in y direction)

formal force:

N = mg cos(theta)

frictional force in X direction

Ff = uk N = uk mg cos(theta)

mg sin(theta) = uk mg cos(theta)

uk = sin(theta)/cos(theta) = tan(theta)

Hence, uk = tan(theta)

An object is sliding down from the ramp inclined at theta = 30 degree to the horizontal. What will be coefficient of kinetic friction acting on the object if the mass of the object is 2 kg and its is siding downwards.

from the above derivation we have:

uk = tan(theta) = tan30 = 0.577

Hence, uk = 0.577