Pulling a Block

Force Acting	Horizontal Component	Limiting Friction	Frictional Force acting

Angle and Start buttons can be clicked when the text is blue .The text turns black when the block is moving. Buttons will be inactive when the text is black. Angle can be incremented from 0° to 60° in steps of 10°. Intially the angle is set to 0°.
Please press start to begin the animation.The force gradually increases in steps of 0.05 N (0.01 N if μ=0.2 and 0.02 N if μ = 0.4) till the block moves. The value of the force when the block starts moving and the corresponding angle are shown in a table in the graph area on the right.
The angle text button turns blue and can now be clicked to increment the angle. Press start again. Repeat till you reach the final value of 60°. A graph will be drawn now.
Values of μ can be changed by using the slider.
Red button resets the animation and sets the angle to 0°. ×

The block shown at top left is lying on a rough horizontal surface. A force can be applied to the block at any angle with the horizontal and it can be increased from an initial zero value. As the force is increased the frictional force also increases, reaching a limiting value for certain value of applied force. These values are tabulated in the table at the bottom right. If the force is increased beyond a certain value the block starts moving. This value is plotted in the graph.

Once set in to motion, the frictional force drops to a lower value ( Kinetic friction being less than the static friction) and the block moves with an acceleration.

If the angle at which the force is applied is increased, the force required to set the block in to motion decreases up to a certain value of this angle and then increases. This can be observed in the graph. You should notice that it is easiest to move the body if the force is applied at a certain angle.

So this is what you should do. Set the frictional coefficient to some value, set the angle of application and then increase the force. Observe the values in the table. Notice that friction acting is less than the limiting frictional force till motion commences and is equal to the horizontal component of the force acting till the motion commences. At some value of the applied force the block starts moving because frictional force can not grow beyond its limiting value. You see the value of the applied force when the block is on the verge of motion indicated in the graph. This value is also listed in the table above the graph. (The value shown in the table is assumed to have been arrived at by a little more careful experimentation. The force is to be imagined to have been incremented in very small steps as the block approaches the verge of motion condition and the value noted is the value of force just before the block starts moving. This is so because verge of motion can only be guessed by observing the motion that takes place after that condition is just crossed.)

Change the angle at which the force is applied and repeat the process.

You may repeat this for a different value for coefficient of friction.

Left / Right clicks in the blue area increase/decrease the Force.

Force F applied at an angle θ above the horizontal. When the block is on the verge of motion, force of friction will reach its limiting value of μN.