Friction, Tension & Normal Force
IMAT Interactive Study Tool
Normal Force (\(F_N\))
The normal force is the support force exerted by a surface on an object in contact with it. It always acts perpendicular to the surface.
It's a "push back" force. If you push on a wall, the wall pushes back on you with an equal and opposite normal force. On a horizontal surface, the normal force is often equal to the object's weight, but this is not always true (e.g., on an inclined plane).
On a flat surface: \(F_N = mg\)
On an inclined plane: \(F_N = mg \cos(\theta)\)
Tension (\(T\))
Tension is the pulling force transmitted through a string, rope, cable, or similar object. It is always directed along the rope and away from the object it is pulling.
For a massless, unstretchable rope, the tension is the same at every point along the rope.
Friction (\(F_f\))
Friction is a force that opposes the relative motion or tendency of such motion between surfaces in contact. It always acts parallel to the surface.
- Static Friction (\(F_s\)): Acts on objects at rest. It is a "smart" force that matches the applied force up to a maximum value.
- Kinetic Friction (\(F_k\)): Acts on objects in motion. It is generally a constant value and is usually less than the maximum static friction.
Maximum Static Friction: \(F_{s,max} = \mu_s F_N\)
Kinetic Friction: \(F_k = \mu_k F_N\)
Where \(\mu\) is the coefficient of friction (a property of the surfaces).
Embedded PhET Simulation
Use the interactive simulation below to explore the concepts of force, mass, acceleration, and friction. Try applying different forces to objects of different masses and observe the results.
1. True or False: The normal force on an object is always equal to its weight (\(mg\)).
Example 1: Pulling a Block with Friction
A 10 kg block is pulled horizontally by a rope with a tension of 50 N. The coefficient of kinetic friction between the block and the floor is 0.3. What is the acceleration of the block? (Use \(g = 10 \, m/s^2\)).
Step 1: Calculate the Normal Force and Friction Force.
The surface is horizontal, so the normal force equals the weight: \(F_N = mg = 10 \times 10 = 100 \, N\).
The kinetic friction is: \(F_k = \mu_k F_N = 0.3 \times 100 \, N = 30 \, N\).
Step 2: Calculate the net horizontal force.
The tension pulls to the right, and friction opposes to the left.
\(\sum F = T - F_k = 50 \, N - 30 \, N = 20 \, N\).
Step 3: Use Newton's Second Law (\(F=ma\)) to find acceleration.
\(a = \frac{\sum F}{m} = \frac{20 \, N}{10 \, kg} = 2 \, m/s^2\)
Conclusion: The block accelerates at 2 m/s².
Example 2: Block on an Inclined Plane
A 5 kg block rests on a plane inclined at 30°. The coefficient of static friction is 0.4. Does the block slide? (Use \(g = 10 \, m/s^2\), \(\sin(30^\circ)=0.5\), \(\cos(30^\circ)\approx0.87\)).
Step 1: Calculate the force pulling the block down the incline.
This is the parallel component of gravity: \(F_{g\parallel} = mg \sin(\theta) = 5 \times 10 \times 0.5 = 25 \, N\).
Step 2: Calculate the maximum available static friction force.
First, find the Normal Force: \(F_N = mg \cos(\theta) = 5 \times 10 \times 0.87 = 43.5 \, N\).
Then, find max static friction: \(F_{s,max} = \mu_s F_N = 0.4 \times 43.5 \, N = 17.4 \, N\).
Step 3: Compare the forces.
The pulling force (\(25 \, N\)) is greater than the maximum available friction force (\(17.4 \, N\)).
Conclusion: Yes, the block will slide down the incline.