A block of mass M is placed on a surface of table and is pulled by a force F acting at an angle F with horizontal . Find acceleration of block if coefficient of

Question

A block of mass M is placed on a surface of table and is pulled by a force F acting at an angle Φ with horizontal . Find acceleration of block if coefficient of friction between surface and block is µ . what should be the angle for which we need minimum force to just move the block?

 

As we know force of friction is = µR where R is Normal reaction . In upper problem what should we the value of R. Mg or (Mg-FsinΦ) . Please make it clear for me it is very confusing problem for me . what value of normal reaction we should take in finding force of friction .

Answer 1

Tony,

         If you draw a free body diagram of the block showing all the forces acting then pick an x and y direction say y is perpendicular to the top surface of the block and x is perpendicular to the front face of the block then you add all the force component in the y and directions and set each equal to the mass time the acceleration component.

 

Forces in the y direction: Fsin(Φ) + N -Mg =0   i.e. the block does not accelerate in the y direction 

Forces in the x direction: μN-Fcos(Φ) =ma_x

Now you can solve the first equation for N and substitute in the second and find the angle that a_x=0.

The way you do mechanics is to pick a coordinate system, draw a diagram showing all the forces acting, find the components and set them equal to the mass of the body time its vector acceleration.

 

Hope this helps

 

Jim