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2.3 Contact Forces

6 min readdecember 23, 2022

Erin Brzusek

Erin Brzusek

Daniella Garcia-Loos

Daniella Garcia-Loos

Erin Brzusek

Erin Brzusek

Daniella Garcia-Loos

Daniella Garcia-Loos

Types of Contact Forces

A contact force is a type of force that arises when two objects are in physical contact with each other. These forces can be either attractive or repulsive, and they arise due to the interaction between the particles that make up the objects. These forces will provide a foundation for the rest of this course, so get comfortable with them. And maybe brush up on your trigonometry!

Examples of include:

  1. : This is a force that opposes the motion of an object when it is in contact with a surface. is what allows us to walk on the ground, hold onto objects, and drive cars.

  2. : This is a force that acts perpendicular to a surface and supports the weight of an object resting on that surface. For example, when you sit on a chair, the chair exerts an upward on you to support your weight.

  3. : This is a force that acts along a rope or wire and is used to transmit a pulling force from one object to another. For example, when you pull on a rope to lift a heavy object, the rope exerts a force on the object.

Key Concept: - forces that occur when an object or system is in direct contact with another

Force

Description

Occurs when an object is pulled by a rope, string, or chain

Occurs when two surfaces are trying to slide (static) or sliding (kinetic)

Normal

Occurs when an object is in contact with a surface

Spring

Occurs when a spring or an elastic material is compressed or extended

When creating free-body diagrams, we must understand how to correctly illustrate the direction of these

  • - The direction the rope, string, or chain is attached

  • - opposes the direction of motion

  • Normal - Perpendicular to the surface

  • Spring - Opposes the direction of the extension or compression

    https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%202020-03-21%20at%207.14.46%20PM.png?alt=media&token=aa14072d-863d-4f78-98b6-02c1571e82d3

Image Courtesy of studyphysics.ca

The image above shows the free-body diagram of an object on an inclined plane, Weight is always drawn directly downwards. is drawn opposite the direction of motion, and is perpendicular to the surface. 

🎥Watch: AP Physics 1 - Introduction to Forces Part 2

Things to remember about normal forces:

  • A is a force that acts perpendicular to a surface and supports the weight of an object resting on that surface.

  • The arises due to the interaction between the particles that make up the object and the surface it is in contact with.

  • The is always present when an object is resting on a surface.

  • The is important because it determines the amount of other forces that can act on an object. For example, the determines the amount of that can act on an object.

Example Problem:

A box of mass 10.0 kg is placed on a ramp inclined at an angle of 30° to the horizontal. Calculate the acting on the box.

To solve this problem, we can use the equation for the , which is given by Fn = Fgcosθ, where Fn is the , Fg is the gravitational force, and θ is the angle of the ramp. The gravitational force is given by the equation Fg = mg, where Fg is the weight and g is the acceleration due to gravity.
Plugging in the given values, we have: Fg = (10.0 kg)(9.80 m/s^2) = 98.0 N
The is given by the equation Fn = Fgcosθ, so: Fn = (98.0 N)cos(30°) = 86.6 N
Therefore, the acting on the box is 86.6 N.

Key Concept: Hooke’s Law - the amount of stretching or elongation of a string when a mass is attached to it is directly proportional to the applied weight. 

Equation: F = -kx

  • Where k is the spring constant in units of Newtons per Meter (N/m) and x is the stretching or elongation of the spring beyond its original length. 

Example Problem:

How much force is needed to pull a spring with a spring constant of 10 N/m a distance of 20 m?

  • Equation: F = kx

Since we’re looking for the force required to pull the spring apart, we don’t need the minus sign!

  • k = 10 N/m

  • x = 20 m

F = 10 N/mᆞ20m

Answer: The force needed is 200N

🎥Watch: AP Physics 1 - Unit 2 Streams

Key Concept: : A key factor in understanding the setup of the equations surrounding Newton’s Laws is familiarizing oneself with . acts as the force that opposes the motion or attempted motion of an object. 

The equation for is given by Ff <= μ*n where μ (Greek letter mu) is the coefficient of either static or . is present if a problem mentions a “rough” surface, or specifically states the coefficient of static or

Equation: Ff <= μ*n

Here are the main differences between and :

  • is the that acts on an object when it is not moving, or when it is in a state of static equilibrium.

  • is the that acts on an object when it is moving.

  • acts to prevent an object from moving, while acts to oppose the motion of an object.

  • is generally larger than . This means that it takes more force to start an object moving from rest than it does to keep it moving at a constant speed.

  • is always present when an object is resting on a surface. is always present when an object is moving on a surface.

  • The amount of and depends on the materials of the two surfaces in contact.

Example Problem:

A block of mass 4.00 kg is placed on a ramp inclined at an angle of 30° to the horizontal. The coefficient of between the block and the ramp is 0.400. Calculate the acceleration of the block as it slides down the ramp.

To solve this problem, we need to use the equation of motion F = ma, where F is the total force acting on the object, m is the mass of the object, and a is the acceleration. In this case, the total force acting on the block is the sum of the gravitational force, the , and the force of .
The gravitational force is given by the equation Fg = mg, where Fg is the weight and g is the acceleration due to gravity. Plugging in the given values, we have:
Fg = (4.00 kg)(9.80 m/s^2) = 39.2 N
The is given by the equation Fn = Fgcosθ, where Fn is the , Fg is the gravitational force, and θ is the angle of the ramp. Plugging in the given values, we have:
Fn = (39.2 N)cos(30°) = 34.6 N
The force of is given by the equation Ff = μFn, where Ff is the force of , μ is the coefficient of , and Fn is the . Plugging in the given values, we have:
Ff = (0.400)(34.6 N) = 13.8 N
The total force acting on the block is the sum of the gravitational force, the , and the force of , so:
F = Fg + Fn + Ff = 39.2 N + 34.6 N + 13.8 N = 87.6 N
Now, we can use the equation of motion F = ma to calculate the acceleration of the block:
a = F/m = (87.6 N)/(4.00 kg) = 21.9 m/s^2
Therefore, the acceleration of the block as it slides down the ramp is 21.9 m/s^2.

FRQ PRACTICE:

Want more practice with ? Check out this FRQ from the 2017 AP Physics 1 exam. 

Key Terms to Review (12)

Coefficient of Friction (μ)

: The coefficient of friction is a value that represents the amount of friction between two surfaces in contact. It quantifies how easily one surface slides over another and depends on factors like roughness and material properties.

Contact Forces

: Contact forces are types of external forces that occur when two objects physically touch each other and interact through direct contact.

Force of Friction Equation (Ff=μFn)

: The force of friction equation states that the force of friction (Ff) acting on an object is equal to the coefficient of friction (μ) multiplied by the normal force (Fn).

Friction

: Friction is a force that opposes relative motion between two surfaces in contact. It arises due to microscopic irregularities between surfaces and can cause objects to slow down or come to rest.

Gravitational Force (Fg=mg)

: Gravitational force refers to the attractive force between two objects with mass. It depends on their masses and decreases as their distance increases. The formula for gravitational force is Fg = mg, where Fg represents the gravitational force, m represents mass, and g represents the acceleration due to gravity.

Hooke's Law

: Hooke's Law states that within the elastic limit, the force required to stretch or compress an elastic material (like a spring) is directly proportional to its displacement from equilibrium.

Kinetic Friction

: Kinetic friction is the force that opposes the motion of an object when it is already moving. It occurs between two surfaces in contact and depends on the coefficient of kinetic friction and the normal force.

Newton's Second Law (F=ma)

: Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In simpler terms, it explains how the motion of an object changes when a force is applied to it.

Normal Force

: The normal force is the force exerted by a surface to support the weight of an object resting on it. It acts perpendicular to the surface.

Normal Force Equation (Fn=Fgcosθ)

: The normal force equation states that the normal force (Fn) acting on an object is equal to the weight of the object (Fg) multiplied by the cosine of the angle (θ) between the object and a horizontal surface.

Static Friction

: Static friction is the force that prevents two surfaces from sliding past each other when they are not moving relative to each other. It acts parallel to the contact surface and opposes any applied force trying to initiate motion.

Tension

: Tension is a pulling force transmitted through a string, rope, cable, or any flexible connector. It acts along the direction of the connector and has equal magnitude at both ends.

2.3 Contact Forces

6 min readdecember 23, 2022

Erin Brzusek

Erin Brzusek

Daniella Garcia-Loos

Daniella Garcia-Loos

Erin Brzusek

Erin Brzusek

Daniella Garcia-Loos

Daniella Garcia-Loos

Types of Contact Forces

A contact force is a type of force that arises when two objects are in physical contact with each other. These forces can be either attractive or repulsive, and they arise due to the interaction between the particles that make up the objects. These forces will provide a foundation for the rest of this course, so get comfortable with them. And maybe brush up on your trigonometry!

Examples of include:

  1. : This is a force that opposes the motion of an object when it is in contact with a surface. is what allows us to walk on the ground, hold onto objects, and drive cars.

  2. : This is a force that acts perpendicular to a surface and supports the weight of an object resting on that surface. For example, when you sit on a chair, the chair exerts an upward on you to support your weight.

  3. : This is a force that acts along a rope or wire and is used to transmit a pulling force from one object to another. For example, when you pull on a rope to lift a heavy object, the rope exerts a force on the object.

Key Concept: - forces that occur when an object or system is in direct contact with another

Force

Description

Occurs when an object is pulled by a rope, string, or chain

Occurs when two surfaces are trying to slide (static) or sliding (kinetic)

Normal

Occurs when an object is in contact with a surface

Spring

Occurs when a spring or an elastic material is compressed or extended

When creating free-body diagrams, we must understand how to correctly illustrate the direction of these

  • - The direction the rope, string, or chain is attached

  • - opposes the direction of motion

  • Normal - Perpendicular to the surface

  • Spring - Opposes the direction of the extension or compression

    https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%202020-03-21%20at%207.14.46%20PM.png?alt=media&token=aa14072d-863d-4f78-98b6-02c1571e82d3

Image Courtesy of studyphysics.ca

The image above shows the free-body diagram of an object on an inclined plane, Weight is always drawn directly downwards. is drawn opposite the direction of motion, and is perpendicular to the surface. 

🎥Watch: AP Physics 1 - Introduction to Forces Part 2

Things to remember about normal forces:

  • A is a force that acts perpendicular to a surface and supports the weight of an object resting on that surface.

  • The arises due to the interaction between the particles that make up the object and the surface it is in contact with.

  • The is always present when an object is resting on a surface.

  • The is important because it determines the amount of other forces that can act on an object. For example, the determines the amount of that can act on an object.

Example Problem:

A box of mass 10.0 kg is placed on a ramp inclined at an angle of 30° to the horizontal. Calculate the acting on the box.

To solve this problem, we can use the equation for the , which is given by Fn = Fgcosθ, where Fn is the , Fg is the gravitational force, and θ is the angle of the ramp. The gravitational force is given by the equation Fg = mg, where Fg is the weight and g is the acceleration due to gravity.
Plugging in the given values, we have: Fg = (10.0 kg)(9.80 m/s^2) = 98.0 N
The is given by the equation Fn = Fgcosθ, so: Fn = (98.0 N)cos(30°) = 86.6 N
Therefore, the acting on the box is 86.6 N.

Key Concept: Hooke’s Law - the amount of stretching or elongation of a string when a mass is attached to it is directly proportional to the applied weight. 

Equation: F = -kx

  • Where k is the spring constant in units of Newtons per Meter (N/m) and x is the stretching or elongation of the spring beyond its original length. 

Example Problem:

How much force is needed to pull a spring with a spring constant of 10 N/m a distance of 20 m?

  • Equation: F = kx

Since we’re looking for the force required to pull the spring apart, we don’t need the minus sign!

  • k = 10 N/m

  • x = 20 m

F = 10 N/mᆞ20m

Answer: The force needed is 200N

🎥Watch: AP Physics 1 - Unit 2 Streams

Key Concept: : A key factor in understanding the setup of the equations surrounding Newton’s Laws is familiarizing oneself with . acts as the force that opposes the motion or attempted motion of an object. 

The equation for is given by Ff <= μ*n where μ (Greek letter mu) is the coefficient of either static or . is present if a problem mentions a “rough” surface, or specifically states the coefficient of static or

Equation: Ff <= μ*n

Here are the main differences between and :

  • is the that acts on an object when it is not moving, or when it is in a state of static equilibrium.

  • is the that acts on an object when it is moving.

  • acts to prevent an object from moving, while acts to oppose the motion of an object.

  • is generally larger than . This means that it takes more force to start an object moving from rest than it does to keep it moving at a constant speed.

  • is always present when an object is resting on a surface. is always present when an object is moving on a surface.

  • The amount of and depends on the materials of the two surfaces in contact.

Example Problem:

A block of mass 4.00 kg is placed on a ramp inclined at an angle of 30° to the horizontal. The coefficient of between the block and the ramp is 0.400. Calculate the acceleration of the block as it slides down the ramp.

To solve this problem, we need to use the equation of motion F = ma, where F is the total force acting on the object, m is the mass of the object, and a is the acceleration. In this case, the total force acting on the block is the sum of the gravitational force, the , and the force of .
The gravitational force is given by the equation Fg = mg, where Fg is the weight and g is the acceleration due to gravity. Plugging in the given values, we have:
Fg = (4.00 kg)(9.80 m/s^2) = 39.2 N
The is given by the equation Fn = Fgcosθ, where Fn is the , Fg is the gravitational force, and θ is the angle of the ramp. Plugging in the given values, we have:
Fn = (39.2 N)cos(30°) = 34.6 N
The force of is given by the equation Ff = μFn, where Ff is the force of , μ is the coefficient of , and Fn is the . Plugging in the given values, we have:
Ff = (0.400)(34.6 N) = 13.8 N
The total force acting on the block is the sum of the gravitational force, the , and the force of , so:
F = Fg + Fn + Ff = 39.2 N + 34.6 N + 13.8 N = 87.6 N
Now, we can use the equation of motion F = ma to calculate the acceleration of the block:
a = F/m = (87.6 N)/(4.00 kg) = 21.9 m/s^2
Therefore, the acceleration of the block as it slides down the ramp is 21.9 m/s^2.

FRQ PRACTICE:

Want more practice with ? Check out this FRQ from the 2017 AP Physics 1 exam. 

Key Terms to Review (12)

Coefficient of Friction (μ)

: The coefficient of friction is a value that represents the amount of friction between two surfaces in contact. It quantifies how easily one surface slides over another and depends on factors like roughness and material properties.

Contact Forces

: Contact forces are types of external forces that occur when two objects physically touch each other and interact through direct contact.

Force of Friction Equation (Ff=μFn)

: The force of friction equation states that the force of friction (Ff) acting on an object is equal to the coefficient of friction (μ) multiplied by the normal force (Fn).

Friction

: Friction is a force that opposes relative motion between two surfaces in contact. It arises due to microscopic irregularities between surfaces and can cause objects to slow down or come to rest.

Gravitational Force (Fg=mg)

: Gravitational force refers to the attractive force between two objects with mass. It depends on their masses and decreases as their distance increases. The formula for gravitational force is Fg = mg, where Fg represents the gravitational force, m represents mass, and g represents the acceleration due to gravity.

Hooke's Law

: Hooke's Law states that within the elastic limit, the force required to stretch or compress an elastic material (like a spring) is directly proportional to its displacement from equilibrium.

Kinetic Friction

: Kinetic friction is the force that opposes the motion of an object when it is already moving. It occurs between two surfaces in contact and depends on the coefficient of kinetic friction and the normal force.

Newton's Second Law (F=ma)

: Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In simpler terms, it explains how the motion of an object changes when a force is applied to it.

Normal Force

: The normal force is the force exerted by a surface to support the weight of an object resting on it. It acts perpendicular to the surface.

Normal Force Equation (Fn=Fgcosθ)

: The normal force equation states that the normal force (Fn) acting on an object is equal to the weight of the object (Fg) multiplied by the cosine of the angle (θ) between the object and a horizontal surface.

Static Friction

: Static friction is the force that prevents two surfaces from sliding past each other when they are not moving relative to each other. It acts parallel to the contact surface and opposes any applied force trying to initiate motion.

Tension

: Tension is a pulling force transmitted through a string, rope, cable, or any flexible connector. It acts along the direction of the connector and has equal magnitude at both ends.


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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.