Contact Forces 

Contact forces result from the interaction of one object touching another object, and they arise from interatomic electric forces. These forces include tension, friction, normal, spring (Physics 1), and buoyant (Physics 2).

Review

Let's review some basic contact forces from Physics 1 and remind ourselves of what they are! 

Contact Forces - forces that occur when an object or system is in direct contact with another. 

• Tension - Occurs when an object is pulled by a rope, string, or chain.

• Friction - 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 Let's look at how to draw these on FBD! 

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

• Friction - opposes the direction of relative motion

• Normal - Perpendicular to the surface

• Spring - Opposes the direction of the extension or compression

Some other basic concepts not specifically in the AP Physics 2 curriculum but the writers may ask you to recall from Physics 1! 

1. 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. 

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.

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

The equation for friction is given by

where μ (Greek letter mu) is the coefficient of either static or kinetic friction and N is the normal force.  

Friction is present if a problem mentions a “rough” surface, or specifically states the coefficient of static or kinetic friction.

Buoyancy is a contact force exerted by a fluid on an object that is submerged or floating in the fluid. The buoyant force is equal to the weight of the fluid displaced by the object, and it acts in the opposite direction of gravity. This means that if an object is denser than the fluid around it, it will sink, and if it is less dense, it will float. Archimedes' Principle is a statement that describes the relationship between buoyancy and the weight of fluid displaced.

Contact forces can be divided into two categories: non-conservative and conservative forces. Non-conservative forces, such as friction and air resistance, convert some of the energy of motion into other forms of energy, such as heat. Conservative forces, such as tension and normal force, do not convert energy but instead store it in the form of potential energy, which can be recovered if the force is removed.

Practice Problems

Example Problem #1: 

A box with a mass of 20 kg is sitting on a horizontal surface. A horizontal force of 60 N is applied to the box to move it. Calculate the force of friction acting on the box.

Solution: To calculate the force of friction, we can use the equation: friction force = friction coefficient x normal force. The normal force is equal to the weight of the box, which is equal to the mass of the box times the acceleration due to gravity (g). So, normal force = 20 kg x 9.8 m/s^2 = 196 N.

Since the force applied to the box is not enough to overcome the force of friction, the box will not move. Therefore, the force of friction acting on the box is equal to the force applied to it, which is 60 N.

Example Problem #2:

A rope is hanging vertically from a pulley with a mass of 10 kg attached to the end of it. The rope has a tension of 200 N. Calculate the weight of the pulley

Solution: The tension in the rope is equal to the weight of the pulley, which can be calculated using the equation: weight = tension / g.

We know that tension = 200 N

g = 9.8 m/s^2

The weight of the pulley = 200 N / 9.8 m/s^2 = 20.4 kg

Example Problem #3:

A wooden block with a density of 600 kg/m^3 and a volume of 0.02 m^3 is placed in a swimming pool filled with water (density = 1000 kg/m^3). Calculate the buoyant force acting on the block.

Solution: The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid that is displaced by the object. The weight of the fluid that is displaced can be calculated using the equation: weight of fluid = density of fluid x volume of fluid x g.

We know that

density of water = 1000 kg/m^3

volume of block = 0.02 m^3

g = 9.8 m/s^2

The weight of the fluid that is displaced = 1000 kg/m^3 x 0.02 m^3 x 9.8 m/s^2 = 19.6 N

The buoyant force acting on the block is equal to the weight of the fluid that is displaced, which is 19.6 N.