Question

Two masses are connected by a light string, which passes over a frictionless pulley as shown in fig .3 on a the chalkboard. The inclined plane is rough. When m1=10kg , m2 = 3.0 kg and theta = 60degrees, the 10 kg mass moves down the inclined plane and accelerates down the nclined pane at a rate of 2.0m/s^2. Find a) the tension in the string. b)the coefficient of kinetic friction between the 10 kg mass and the inclined plane.

Answer 1

The set up of the problem is as shown in the figure above, where T is the tension in the string, and is the frictional force.

a) Now in order to find the tension in the string, let us take look at the equation of motion of the mass, . The tension and the acceleration of the string mass system is in the same direction against the force of gravity, hence,

ie,

given : a=2m/s^2

Hence,

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b) To find teh coefficient of kinetic friction, we have to take a look at the mass . Here, we can see that the force of friction and the tension are acting againt the direction of motion and the sine component of the gravitaional force is acting along the direction of motion, hence

ie,

Substituting the known values,

Now the frictional force is givn by , N is the normal force ofn the mass and is the coefficient of static friction

Here,

Hence,