Question

I am in physics and do not understand Newton's third law when expressions like mgsintheta are used. How do you know what to subtract and what to add when doing problems?

Answer 1

Let consider the situation where an object is moving on the rough frictious surface of a inclined plane as shown in figure. corresponding x axs and y axis is shown on figure. Now you have to draw free body diagram i.e. have to show forces along x and y axis. in this situation forces along +ve x axis is mgsin(theta). as we know that friction force is always acts opposite to the direction of motion then net force acting on the object along x axis is mgsin(theta) - Fr, where Fr is frictional force. If acceleration of the object is a along x axis then ma= mgsn(theta) - Fr .........(1) (where m is mass of the object and g is gravitational acceleraton , theta is the inclined angle)

now along y axs:

there is only normal force N along +ve y axis and mgcos(theta) aong - ve y axis. since there is no motion along y axis thus N - mgcos(theta)=0 or, mgcos(theta)=N................(2)

We know that frictional force is equal to the Normal force multiplied by coefficient of friction.

so Fr= u*N= u*mgcos(theta) .............( 3) (from eqn 2)

hence we can write from equation 1

ma= mgsin(theta)- u*mgcos(theta)...............(4)

please give a thumbs up. and if you have any doubt then pls comment.