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Causes of Static Friction
When there is no relative motion between the contact point but there is tendency of relative motion between the surfaces then static friction force acts.
Let’s do some TRUE/FALSE based on what we’ve covered so far.
Q6. State TRUE or FALSE.
Statement – When there is no relative motion between the two objects, kinetic friction force will not act.
Ans : TRUE
Hint – This is covered under definition of kinetic friction.
Q7. State TRUE or FALSE.
When there is no relative motion between the contact points of object and surface then static friction force will act.
Ans : FALSE
Explanation – Static friction acts when there is tendency of relative motion. Above statement says there is no relative motion which doesn’t clarify that if there is any tendency of relative motion or not. If there is no relative motion and there is no tendency of relative motion as well then static friction force will not act nor kinetic friction. If there is tendency of relative motion, (but relative velocity = 0), static friction force will act but kinetic friction will not.
Motto of static friction – Don’t let relative motion start.
Always remember static motion is self-adjusting force. It can adjust direction as well as it’s magnitude.
Direction of static friction
To decide the direction of static friction, first assume all surfaces to be frictionless (i.e. smooth) and check which object has tendency to which direction. Then check what would have been direction of relative motion, apply static friction opposite to that direction.
So, assume that what would have happened if there was no friction. Thus we would know in which direction tendency of relative motion is there. Static friction always acts opposite to the tendency of relative motion.
Tendency of relative motion will be decided by resultant of contact force parallel to the contact surface.
In above case, find out direction of friction.
Let’s assume all surfaces are smooth. Hence there won’t be any friction force. As force is acting in right direction, object will start moving in right direction. Relative motion of object with respect to contact surface will be in right direction, hence kinetic friction would have act in left direction.
Now we know that there is tendency of relative motion in right direction, hence static friction force will act in left direction.
Magnitude of static friction
Maximum value of static friction will act when slipping is just about to start between two surfaces.
- Under the condition of just slipping the two contact surfaces will have same acceleration.
- Whenever the static friction force acts between the two surfaces, two surfaces will have some acceleration.
Let’s do some examples on static friction –
Find out the acceleration and friction force action on the block.
As always, first draw FBD –
We don’t know if there is relative motion or only tendency of relative motion i.e. we don’t know which type of friction force will act in this case. Let’s find out maximum value of static friction force.
f_max = 0.5 x N = 0.5 x 10g = 0.5 x 100 N = 50 N
Now we know that external force action on the object is less than max value of static friction force, hence in this case object will not move i.e. there is only a tendency of relative motion.
As we know that static friction can take any value between zero to max friction force, in this case to make relative velocity zero, static friction force will be equal and opposite to external force. Hence static friction force = 20 N & acceleration of object = 0.
Find out which type of friction will act and what would be value of acceleration if relative motion is not zero.
Let’s draw FBD first,
Apply force balance in vertical direction, N = 9g = 90 N
Maximum value of friction force = 0.5 x 90 N = 45 N
In this case, value of external force is greater than maximum value of friction force, hence there will be relative motion between contact surface and object will move in left direction with some acceleration. Hence, in this case kinetic friction will act.
Apply force balance in horizontal direction –
50 N – 45 N = 9.a
A = 5/9 m/s^2
Find out acceleration of two blocks. Assume ground is surface, while surface between blocks is rough.
Let’s draw FBD first,
In above cases, we don’t know if kinetic friction will act or static friction. It’s a complicated situation and it’s tough to identify type of friction by observation. Hence we will consider two cases, one with kinetic friction and other with static friction. Results from which case will comply with initial assumption will be correct solution.
Case 1 : Let’s assume there will be slipping between two blocks, hence kinetic friction will act.
Force balance on upper block in vertical direction –
N – 10g = 0 i.e. N = 100 N
Hence, f = 0.5 x 100 = 50 N
Apply force balance equation on upper block in horizontal direction –
50 N – f = 10.a
50 N – 50 N = 0 = 10.a
Hence, a = 0
Apply force balance on second block in horizontal direction –
f = 50 N = 10.a
a = 5 m/s^2 (right direction)
Now let’s check if this complies with our initial assumption –
We have assumed that upper block will be moving in right direction with respect to contact surface (hence friction force was applied in left direction). Similarly second block will move relatively slower than upper block and hence friction force should be applied in right direction on second block.
Now result shows that second block will move faster than upper block. (upper block has acceleration = 0 and second block has acceleration = 5 m/s^2). Hence are result is contradicting with initial assumption. Hence this case is not possible.
Case 2: Let there will be no slipping between two blocks, i.e. static friction force will act and acceleration of both blocks will be same. (Remember – when static friction force is acting, both contact surfaces will have same acceleration, as there won’t be any relative motion).
Apply force balance on both blocks in horizontal direction –
50 N – f = 10.a & f = 10.a
Add both equations –
50 = 20.a
a = 2.5 m/s^2
Hence, f = 10.a = 25 N
Now as per our initial assumption, if static friction force is acting, it’s value should be less than or equal to maximum friction force.
Max friction force = 50 N
i.e. f = 25 N < 50 N
Our assumption is right, i.e. in this case static friction force will act, both the objects will move with same acceleration with a = 2.5 m/s^2 and static friction of f = 25 N.
A man is pushing a static wall with hands as shown in figure. No external force is acting on the man apart from contact forces from wall. Find out direction of friction force on man.
Let’s draw FBD first,
It’s pretty clear from free body diagram than if there won’t be any friction, legs of man will slide in right direction because of normal reaction, i.e. there is tendency of relative motion in right direction hence friction force will act in left direction. Also as acceleration is zero in this case, value of friction force will be equal to that of Normal reaction.
Let’s do a last example which will further clarify few concepts –
Force F is acting on a block as shown in figure, placed on a wedge making an angle with horizontal surface. Surface is rough, take friction coefficient as given in figure.
Find Maximum and Minimum value of force F to stop sliding of block.
You might be wondering why there would be two values of force F to stop sliding. Please note that there will be gravitational force acting on the block in downward direction, and external force F is acting in upward direction, hence block might move in either direction. Because of this friction force might act in either direction as well and because of that in once case F and friction force will act in same direction (resulting in minimum value of F). In other case, block will be sliding in the direction of F, and friction force will act in opposite direction (resulting into maximum value of F).
Let’s take case 1 – Friction is acting opposite to F
Apply force balance perpendicular to the contact surface,
N – 10g sin37 = 0
N = 100 x 3/5 = 60 N
Hence, f = 60 X 0.5 = 30 N
Now, apply force balance parallel to contact surface,
F – 10g cos37 – f = 0
F – 100 x 4/5 – 30 = 0
F = 110 N (max value of F required)
Let’s take case 2 : friction is acting in the direction of F
Force balance will be same in perpendicular direction of contact surface, i.e. f = 30 N
Now, apply force balance in parallel to contact surface,
F + f – 10g cos37 = 0
F = 100 x 4/5 – 30 = 50 N