How to Solve Impending Motion and Static Friction Questions
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
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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 < Fmax
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.
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Solution:
All the forces that are acting on the object are shown in the following diagram
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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
FAQs on Impending Motion in Physics: Definition, Equations & Problems
1. What is impending motion, and how is it determined in Physics as per CBSE 2025–26 syllabus?
Impending motion refers to the condition when an object is just about to start moving but has not yet overcome the maximum static friction. It is determined by checking if the applied force is equal to the maximum static frictional force, calculated as F = μsN, where μs is the coefficient of static friction and N is the normal force. When F equals this value, the object is on the verge of slipping.
2. What are the three states related to friction and motion of a body on a surface?
The three states are:
- No Motion: The body remains at rest; applied force is less than limiting static friction (F < Fs).
- Impending Motion: The applied force equals limiting static friction (F = Fs); the object is about to move.
- Motion: The object starts moving, and the frictional force reduces to kinetic friction (F = μkN).
3. Why does the direction of friction always oppose impending motion?
The direction of friction always opposes impending motion because friction acts to prevent the relative movement between two surfaces. Until motion starts, static friction adjusts itself to exactly balance the applied force, always resisting the direction of intended movement to keep the body at rest.
4. How do you calculate the force required to reach impending motion when given the coefficient of static friction and mass?
To find the force required for impending motion:
- Calculate the normal force (N) using N = mg if horizontal, or adjust for inclined planes.
- Multiply by the coefficient of static friction: F = μsN.
- This force marks the limit before the object starts moving.
5. How can you distinguish between static friction and kinetic friction with examples from impending motion problems?
Static friction is the force that keeps an object at rest, increasing up to its maximum value to resist motion. Kinetic friction applies once movement has started and is generally less than static friction. For example, pushing a box that resists up to a certain force involves static friction; once the box starts sliding, kinetic friction takes over, requiring less force to keep it moving.
6. What are some common misconceptions students have regarding the concept of impending motion?
Common misconceptions include:
- Believing impending motion starts before the static friction limit is reached.
- Confusing the values of static and kinetic friction coefficients.
- Assuming friction always remains constant during motion transition, while it actually drops after motion begins.
7. Why is understanding impending motion important for solving friction-based problems in board exams?
Impending motion is essential because many board exam questions require identifying the exact moment when an object begins to slip, which determines the force calculations. Knowing how to apply the limiting condition (F = μsN) is crucial for accurate answers and scoring on high-weightage Physics questions.
8. How does impending motion relate to equilibrium, and what does unstable equilibrium mean in this context?
When an object is at the point of impending motion, it’s in unstable equilibrium: any further increase in the applied force will result in movement. At this point, static friction is at its maximum, balancing the applied force exactly, but the system is sensitive and will immediately lose balance if conditions change.
9. In what practical situations can the concept of impending motion be observed or applied?
Examples include:
- Trying to push a heavy table just before it slides across the floor.
- Vehicles at rest on a slope, just before the wheels start slipping.
- Machines in factories where precise force is applied for controlled movement without jerking.
10. How should you approach a numerical question where you are asked to determine the force for impending motion on an inclined plane?
Approach such numerical problems by:
- Drawing a free-body diagram.
- Resolving forces parallel and perpendicular to the plane to find normal force and frictional limit.
- Using F = μsN to find the critical force needed to start movement.
