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Kinetic and Static Friction

Lesson ~11 min read 8 MCQs

In simple terms: In simple terms, friction is a force that resists sliding between surfaces. It can be static (preventing movement) or kinetic (opposing movement).

Why this matters

Hey there. I'm Saavi, and we're going to tackle one of the most common forces you experience every day: friction.

Imagine you're helping your friend Maya move into a new apartment in Chicago. There's a heavy bookshelf you need to slide across the hardwood floor. You give it a small push. Nothing. You push a little harder. Still nothing. It feels like the floor is pushing back, refusing to let it budge. Finally, you give it one big shove, and it lurches into motion! And once it's moving, you might even notice it's a little easier to keep it sliding than it was to get it started.

That "stuck" feeling and the "drag" you feel while it's sliding? That's friction in a nutshell. We're about to break down exactly what's happening, why it's harder to start than to continue, and how to calculate these forces for your exam.

Diagram

Friction Force vs. Applied Force A graph plotting Friction Force versus Applied Force. The y-axis is Friction Force from 0 to 12 N. The x-axis is Applied Force from 0 to 15 N. The graph shows a diagonal line from (0,0) to a peak at (10,10), representing static friction. It then drops to a horizontal line at y=7, representing constant kinetic friction. 12 10 7 0 Friction Force, f (N) 0 10 15 Applied Force, F_app (N) Static Region (f_s = F_app) Breaking Point f_s,max = 10 N Kinetic Region (f_k = 7 N)
A graph plots Friction Force versus Applied Force. The friction force increases linearly with the applied force in the static region, reaching a maximum of 10 N. It then drops to a constant 7 N in the kinetic region as the object moves.

Concept map

stateDiagram-v2
    [*] --> AtRest
    AtRest: Object is stationary
    AtRest: f_s = F_app
    AtRest --> Sliding: F_app > f_s,max
    Sliding: Object is moving
    Sliding: f_k = constant
    Sliding --> AtRest: Object stops (v=0)

Core explanation

Friction might seem simple, but it has some important rules. Let's break them down so you're never caught off guard.

What Causes Friction?

On a microscopic level, no surface is perfectly smooth. Imagine zooming in on the bottom of that bookshelf and the floor. You'd see jagged peaks and valleys, like two mountain ranges grinding against each other. Friction is the force that arises from these microscopic imperfections interlocking and resisting motion.

This is also why the type of surfaces matters so much. Pushing a bookshelf on a polished wood floor is one thing; pushing it across a shaggy carpet is another entirely. The "roughness" and chemical properties of the surfaces determine how strongly they'll stick together.

Static Friction: The "Smart" Force

Static friction (f_s) is the force that prevents an object from starting to move. I call it the "smart" or "responsive" force because it only pushes back as hard as it needs to.

Think about the bookshelf again.

  • If you push with 5 N of force and it doesn't move, the static friction force is pushing back with exactly 5 N. The net force is zero.
  • If you increase your push to 30 N and it still doesn't move, static friction has matched you, pushing back with 30 N.

But there's a limit. Eventually, you'll push hard enough to overcome the interlocking microscopic hills and valleys. This limit is called the maximum static friction (f_s,max).

The rule for static friction is an inequality:

|F⃗_f,s| ≤ μ_s|F⃗_n|

Let's unpack this.

  • μ_s is the coefficient of static friction. It's a number with no units that represents the "stickiness" between two specific surfaces at rest. A higher μ_s means more stickiness (like sneakers on a basketball court). A lower μ_s means less (like a puck on an air hockey table).
  • F⃗_n is the Normal Force. This is the perpendicular force the surface exerts on the object. On a flat, horizontal surface with no other vertical forces, F_n is equal in magnitude to the object's weight (mg). But be careful! If you're pushing down on the box, or if it's on an incline, F_n will be different.

Kinetic Friction: The Constant Drag

Once you overcome static friction and the object starts sliding, the type of friction changes to kinetic friction (f_k). This is the force that resists an object's motion when it's already moving.

Kinetic friction is simpler. It has a constant value for a given situation. As the microscopic peaks and valleys slide past each other, they don't have time to settle in and lock up as deeply. This means the kinetic friction force is almost always less than the maximum static friction force.

This is why it feels easier to keep the bookshelf moving than it was to start it!

The formula for kinetic friction is an equation, not an inequality:

|F⃗_f,k| = μ_k|F⃗_n|

  • μ_k is the coefficient of kinetic friction. It represents the "slipperiness" between two surfaces that are sliding against each other.
  • For any given pair of surfaces, μ_k is typically less than μ_s.

A common misconception is that friction depends on the surface area of contact. It doesn't! A wide tire and a narrow tire made of the same rubber on the same road will have the same frictional force, assuming the car's weight is the same. It's about the normal force and the nature of the surfaces, not how much area is touching.

Putting It All Together: The Friction Graph

Let's visualize the whole process with a graph. Imagine we are applying a steadily increasing force (F_app) to a heavy box and plotting the friction force that responds.

Friction Force vs. Applied Force Graph

  1. 1
    Static Region (The Ramp Up)
    As we start pushing from 0 N, the static friction force perfectly matches our push. If we push with 2 N, it pushes back with 2 N. If we push with 8 N, it pushes back with 8 N. This is the diagonal line on the graph where f_s = F_app.
  2. 2
    The Breaking Point (The Peak)
    We keep pushing harder until we hit the maximum static friction, f_s,max. In our graph's example, this happens when we apply 10 N of force. At this exact moment, the box is on the verge of moving.
  3. 3
    The Drop
    The instant the box starts to slide, the friction switches from static to kinetic. Because μ_k < μ_s, the friction force suddenly drops to a lower, constant value. In our example, it drops to 7 N.
  4. 4
    Kinetic Region (The Plateau)
    As long as the box is sliding, the kinetic friction force remains constant at 7 N, no matter how much faster we push it. This is the flat, horizontal line on the graph.

Understanding this graph is crucial. It tells the entire story of friction in one picture.

Worked examples

Let's walk through a couple of problems together. The key is always to identify whether the object is moving or not first.

Example 1

Will It Budge?

A 15 kg wooden crate rests on a wooden floor in a warehouse in Dallas. The coefficient of static friction μ_s between the wood surfaces is 0.5, and the coefficient of kinetic friction μ_k is 0.3. A worker, Priya, pushes horizontally on the crate with a force of 60 N.

(a) What is the magnitude of the friction force on the crate? (b) Will the crate move?

Step 1: Draw a Free-Body Diagram and Find the Normal Force. The forces acting on the crate are:

  • Gravity (F_g = mg) pulling down.
  • The Normal Force (F_n) from the floor pushing up.
  • Priya's push (F_app) horizontally.
  • Friction (f) opposing the push.

Since the floor is horizontal and there are no other vertical forces, the upward and downward forces balance. F_n = F_g = mg F_n = (15 kg)(9.8 m/s²) = 147 N

Step 2: Determine the Maximum Static Friction. Before we can know if it moves, we need to find the "breaking point." f_s,max = μ_s * F_n f_s,max = (0.5)(147 N) = 73.5 N This is the most the floor can push back before the crate starts to slide.

Step 3: Compare the Applied Force to the Maximum Static Friction. Priya is pushing with F_app = 60 N. Our calculated maximum static friction is f_s,max = 73.5 N.

Since F_app < f_s,max (60 N is less than 73.5 N), the crate will not move.

Step 4: Answer the Question. (a) Because the crate doesn't move, the static friction force is simply matching Priya's push. Therefore, the friction force is 60 N. (b) No, the crate will not move.

Common mistake here: Many students would immediately calculate f_s,max (73.5 N) and say that's the friction force. Remember, static friction is responsive! It only uses as much force as it needs.

Example 2

Calculating Acceleration

Let's say Priya gets her coworker, Carlos, to help. Together, they push the same 15 kg crate with a combined horizontal force of 90 N. What is the acceleration of the crate?

Step 1: Check if the Crate Moves. From Example 1, we know the maximum static friction is f_s,max = 73.5 N. Their applied force is F_app = 90 N. Since F_app > f_s,max (90 N is greater than 73.5 N), the crate will move and accelerate.

Step 2: Calculate the Kinetic Friction Force. As soon as the crate starts sliding, the friction switches to kinetic friction. f_k = μ_k * F_n f_k = (0.3)(147 N) = 44.1 N This is the constant frictional force acting on the crate as it slides.

Step 3: Apply Newton's Second Law (ΣF = ma). We'll look at the net force in the horizontal direction. The applied force pushes it forward, and kinetic friction pushes back. ΣF_x = F_app - f_k = ma_x 90 N - 44.1 N = (15 kg) * a_x 45.9 N = (15 kg) * a_x

Step 4: Solve for Acceleration. a_x = 45.9 N / 15 kg a_x = 3.06 m/s²

The crate accelerates forward at 3.06 m/s².

Try it yourself

Ready to try a couple on your own? Don't just jump to the answer; walk through the steps we just practiced.

  1. 1
    The Stubborn File Cabinet
    A 40 kg metal file cabinet stands on a tile floor in an office in Boston. It takes a horizontal push of at least 235 N to get the cabinet to start moving. What is the coefficient of static friction, μ_s, between the cabinet and the floor?
    • Hint: The phrase "at least 235 N to get... moving" is telling you the value of the maximum static friction. Use that to work backward.
  2. 2
    Sledding in the Park
    Aaliyah is pulling her little brother on a sled across a snowy field in Seattle. The sled is moving at a constant velocity. The combined mass of her brother and the sled is 30 kg, and the coefficient of kinetic friction is 0.1. What is the magnitude of the force Aaliyah is pulling with?
    • Hint: What does "constant velocity" tell you about the net force and acceleration? How must the pulling force relate to the kinetic friction force?
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