[Physics Class Notes] on Impending Motion Pdf for Exam

A state of an object just about to slip from a surface is known as impending motion. Such instances occur when static friction reaches its higher limit and is represented by the following equation.

F = µsN

()

However, before moving on with the details of impending motion, first, you must understand static friction.

What is Static Friction?

Static friction refers to the force which can make a body stay at a resting position. Moreover, the static frictional force is a force that is self-operated, which means that static friction will always be opposite and equal to an applied force.

Also, the frictional force’s direction to the Impending motion of bodies is consistently opposite. If the force exerted (P) escalates, then accordingly F (frictional force) also escalates till F < Fs. Here Fs is restricting static frictional force.

Furthermore, if F = Fs, then the object is in a state of unstable equilibrium and begins to move.

Next, take a look at the three different regions of static to moving transition.

The three areas are – impending motion, no motion and motion.

Impending Motion

The impending motion is defined as the state of a body when it is about to slip from any surface. In a similar situation, the static friction will reach its upper limit and is given by the equation

[F = F_{max}=mu _{s}N]

The direction of the frictional force will always be opposite to the Impending relative motion of the surfaces. If the applied force (P) is increased then the frictional force (F) will also get increased, until F < Fₛ (limiting static frictional force). When F = Fₛ then the body is said to possess an unstable equilibrium and said to be in motion.

No Motion 

This is the region till which a body will not slip and stay at rest. Moreover, in this scenario, the entire set-up is in equilibrium. So, the static friction is shown using expressions of equilibrium:

F < F_max

Motion 

In this region, an object begins moving in the direction similar to the direction of applying force. However, over here, frictional force reduces to a lesser value. This low value is termed as kinetic friction. So, it is represented by the expression:

F = Fmax = µkN

Additionally, for a more transparent comprehension, have a look at the solved example below to determine the force needed for impending motion.

Solved Example

1. If the coefficient of static friction is 0.2, determine the force necessary for impending motion up the plane.

()

Solution:

All the forces that are acting on the object are shown in the following diagram

()

The gravitational force acting on the body can be found as follows:

Fg = mg

By substituting the values, we get

Fg = 100 kg × 9.8 m / s² = 980 N

To maintain the equation at equilibrium, the sum of the horizontal forces and the sum of the vertical forces should be zero.

∑Fx = 0 and ∑Fy = 0

By taking the vertical component of forces to calculate the normal force

∑Fy = − Fg + N (1213)− Fs (513) = 0

By substituting the value of the gravitational and the coefficient of static friction,

we get,

∑Fy = −980 + N (1213) − 0.2 N (513)  = 0 

N (1213) − 0.2 (513) N = 980 N

 = 9801311 = 1158 N

The normal force = 1158 N

Now, to find the pushing force let us look at the horizontal forces 

−N  (513) −Fs (1213) + F = 0 

F = N (513) + μN (1213)

F = N (513) + μN (1213)

Substituting the values we get,

F=1158 (513) + (0.2 × 1158) (1213)

  = 659 N

The force required for impending motion, F = 659.

Do It Yourself

1. There are three types of friction problems. One of them is:

(a) Impending motion at a single point of contact (b) No-Impending motion at a single point of contact (c) Impending motion at all points of contact (d) Apparent Impending motion