Impending Motion

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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 resting position. Moreover, 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, frictional force’s direction to the pending 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

As discussed earlier, impending motion is the point on which a surface will slip and in this case, static friction outreaches it’s maximum limit. So, frictional force for two bodies who are in contact with each other is expressed as:

F = Fmax = µsN

  • 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:


  • 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.

Example. Find out the force needed for impending motion in the given diagram. Note that 0.2 is coefficient of static friction

(image will be uploaded soon)

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

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Moreover, free body illustration can be drawn like:

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Gravitational force of acting on the object can be calculated by this following formula:

Fg = mg

Therefore, by putting the values:

Fg = 150 kg × 9.8 m/s2 = 1470 N

In order to maintain the state of equilibrium, both the sum of vertical and horizontal forces has to be zero.

∑Fx = 0 and ∑Fy = 0

Furthermore, consider the vertical components to evaluate N (normal force)

∑Fy = -Fg + N(12/15) – Fs(9/15) = 0

Now, after substituting coefficient of static friction and gravitational force and in the prior equation it is found:

∑Fy = -1470 + (12/15)N - 0.2N(9/15) = 0

Hence, (12/15)N - 0.2(9/15)N = 1470

So, N = 1470 / (12/15 – (0.2× 9/15))

         = 2162N (normal force)

Now, to determine pushing force consider horizontal forces:

-N(9/15) – Fs(12/15) + F = 0

Therefore, F = N(9/15) + µN(12/15)

Thus, by putting the values,

F = 2162x(9/15) + (0.2×2162)12/15


Therefore, the force required for impending motion is 1643 N.

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

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FAQ (Frequently Asked Questions)

1. What is Impending Motion?

Ans. Impending motion refers to the state of a body before it begins to slip down a surface.

2. What Does µK Mean?

Ans. µK means coefficient of kinetic friction. However, it is utilised in the same manner as that of the coefficient of friction.

3. What is Maximum Static Friction?

Ans. The force that keeps a body at a resting position is called static friction. In order to move, the body must overcome static friction. Moreover, maximum static friction for a body is µs times the standard force on that body.