Key Terminology
Force: Push or pull upon an object resulting from the object's interaction with another object. Forces are vectors, which means that they have both direction and magnitude. The base SI unit for force is the Newton (N), which is the force required to accelerate 1kg at 1m/s^2.
Types of forces:
Types of forces:
- Gravity: force between two objects with mass
- Friction: a force opposite the way objects want to slide
- Normal: support force perpendicular to the surface
- Spring: force between a compressed/stretched spring and an object attached to it
- Applied: a force applied on an object
- Tension: a force transmitted through a rope/string
Identifying Interactions:
System Schema
A system schema is a visual way to keep track of the objects in a system and how they interact. In the system schema, each object is a circle and every force is a line connecting two circles.
Force Diagram (Free Body Diagram)
A visual way to keep track of the forces and the direction of these forces that act upon an object. Represent the object of interest (in this case the skateboard) and represent it with a dot. Draw an arrow for each force acting on the object from the dot to the direction the force acts on the object. Label the force with the TYPE of force, BY an object ON the object of interest.
From: https://www.frostphysics.org/uploads/3/8/3/5/38359885/screen-shot-2019-01-23-at-3-48-46-pm_orig.png (thanks Mr. Frost :D)
It is often useful to draw a Force Table to keep track of the magnitude of the forces that act upon the object of interest in both the X and Y direction.
Newton's First Law of Motion
Newton's First Law of Motion, also known as the Law of Inertia, states that an object will continue to move at a constant velocity unless it feels an unbalanced push or pull. Inertia is an object's tendency to resist change in motion (acceleration).
Newton's First Law of Motion can easily be visualized with a hover puck
From: https://i.pinimg.com/originals/95/2e/ae/952eae0d937ca1245702f001f0d28617.jpg
When we roll a ball across a table, we see that the ball eventually comes to a stop. Which is why some people might be confused about the First Law, which implies that the ball will continue rolling forever. However, we often forget about the friction that also acts on the ball, which creates an unbalanced force acting on the ball thus its acceleration changes. On the other hand, a hover puck hovers above the surface with negligible friction and air resistance, so when you push it, you accelerate it and once you stop pushing, it would continue to move with constant velocity.
An object's inertia also depends on its mass. The more massive an object is, the greater its resistance to a change in motion (inertia). This makes logical sense as it is harder to accelerate a heavier object like a boulder compared to a light object like a cup.
Newton's Second Law of Motion
In the Unbalanced Forces lab (see "Lab" - > "Unbalanced Forces Lab"), my lab partners and I carried out experiments and observed the relationship between mass and acceleration and net force and acceleration. The summary is that:
- The more an object's mass, the more inertia it has and the less acceleration it has
- The more net force an object experiences, the more the acceleration it has
Graphs from "Unbalanced Forces Lab" which show the proportional relationship between net force and acceleration and the inverse relationship between total mass and acceleration.
Newton's Third Law of Motion
Newton's Third Law states that whenever there is an interaction between two forces, there is a force upon each of the objects; these two objects each feel the same magnitude force from the other, but in opposite direction.
From "Flipping Physics"
The forces F21 and F12 are Newton Third Law pairs. The force exerted by the ball on the person has a equal force of the same magnitude but in the opposite direction exerted by the person on the ball.
However, there are some common misconceptions about third law pairs:
For example, a book sitting stationary on a table experiences the force of gravity and the normal force of the table. These forces are equal in magnitude and opposite in direct, but are NOT a Newton Third Law pair since the forces act on the same object. The third law pairs in this example are: 1) the normal force caused by the table on the book and the force that the book exerts on the table and 2) the force of gravity exerted by the earth on the book and the force of gravity exerted by the book on the earth.
For example, a book sitting stationary on a table experiences the force of gravity and the normal force of the table. These forces are equal in magnitude and opposite in direct, but are NOT a Newton Third Law pair since the forces act on the same object. The third law pairs in this example are: 1) the normal force caused by the table on the book and the force that the book exerts on the table and 2) the force of gravity exerted by the earth on the book and the force of gravity exerted by the book on the earth.
Force Calculations
Key Formulas:
- ∑F = ma, Newton's Second Law of Motion explained above.
- Fg = mg, where Fg is the force of gravity (in N), m is mass (in kg) of the object and g is the acceleration due to gravity on Earth (which is around 9.81 m/s^2).
- Fs = -k * delta x, Hooke's law, where Fs is the spring force (in N), k is the spring constant of the spring and delta x is the stretch/compression of the spring (in m). This formula is useful to calculate the spring force of a spring. Notice how there is a negative sign in the right side of the equation, this is because spring force is a resistive force and acts in the direction opposite to the stretch/compression since the spring wants to return to equilibrium.
- Ff = μ * Fn, where Ff is the force of friction, μ (pronounced "mew") is the coefficient of friction and Fn is the normal force.
Solving Force Problems
Five steps:
- Draw the free body diagram
- Break forces into components
- Redraw the free body diagram
- Sum the forces again (in the perpendicular direction or y direction depending on the problem)
- Sum the forces (in the parallel direction or x direction depending on the problem)
For example, in this scenario, a father is pulling his child on a sled through the grass with a string at an angle theta.
The first step is to draw the free body diagram and label the forces. The forces acting on the child are: the normal force of the ground, the force of gravity, the tension force of the rope (which is at an angle), and the force of friction.
Since the force of tension is at an angle, the second step would be to break this force into x and y components. We can find the x and y components by using trigonometry, namely sin(theta) = Opposite/Hypotenuse and cos(theta) = Adjacent/Hypotenuse. Using these formulas, we find that the force of tension in the y direction is equal to the total force of tension times sin(theta) and the force of tension in the x direction is equal to the total force of tension times cos(theta). The third step is to redraw the force diagram with the components we just found to make a clearer visual representation of the problem. The fourth step is to sum up the forces in the y direction and the fifth step is to sum up the forces in the x direction.
Note: Images are from "Flipping Physics"
Note: Images are from "Flipping Physics"
Representations of motion and Force models
An object could be one of three things:
Using Newton's Second Law, ∑F = ma, we can conclude that the net force acting on an object is zero when the object is stationary and moving with a constant velocity, which is a useful fact when solving problems with forces and motion.
- Stationary (motionless) with an constant velocity of zero and constant acceleration of zero
- Moving with a constant non-zero velocity and zero acceleration
- Accelerating
Using Newton's Second Law, ∑F = ma, we can conclude that the net force acting on an object is zero when the object is stationary and moving with a constant velocity, which is a useful fact when solving problems with forces and motion.
Solving Problems with Forces and Motion
Consider the following example:
It is very important to draw the system schema and identify the forces and objects at play
Then draw the force diagram to clarify the directions of the forces acting on the object of interest
Then use a force table to calculate the total force or if you know the total force, use this information with other known forces to find the unknown magnitude of any remaining force. In this case, it is given that the wagon travels at a constant velocity, which means that the net force is zero. We also know that the force applied by the horse on the wagon is 100N, with these two pieces of information we can find the friction force, which is Total Force (in the x-direction) minus Applied Force = -100N. The force of gravity acting on the wagon is 55kg (the mass of the wagon) times -g (the acceleration due to gravity and in the downwards direction) which is -550N. The wagon does not accelerate in the y direction (i.e. the total force in the y direction is zero) so therefore we know that the normal force is 550N to match the force of gravity.
Consider another example:
Draw the force diagram...
Then create the force table. In this case, when we sum up the forces in the x-component, we have a net force of -15N left, which means that the object is accelerating. Using Newton's Second Law, we can find that this acceleration is -15N/3.3kg = -4.5 m/s^2.
Note: All images in this section are from OneNote.