A person standing on a horizontal floor feels two forces: the downward pull of gravity and the upward supporting force from the floor.
A person weighing 800 N steps onto a scale on the floor of an elevator car.
A 20 N block is being pushed across a table.
The acceleration of the block can be found if the table's coefficient of kinetic friction is less than 0.4.
A box and a ramp have the same coefficients of static friction.
The ramp has an incline angle of 30o.
If a massless pulley is used, determine the acceleration of the blocks after they are released from rest.
If all of the forces acting on an object balance so that the net force is zero, the object's direction of motion can change, but not its speed.
On the surface of the Moon, there is a horizontal table with an identical block at rest.
There is a crate of mass on the floor.
There is a coefficient of static friction between the crate and the floor.
There are two crates, one on the bottom and one on the top.
The crates have the same mass.
The crate is being pulled across the floor by a rope.
Assume that the pulley is massless.
To slide up the ramp at constant speed.
There is no need for forces to maintain motion.
Whether that means speeding up, slowing down, or changing direction is up to the forces.
The following strategy is used to solve almost any Second Law problem.
If it helps, make a sketch.
It's important to make a free-body diagram.
Define an appropriate coordinate system.
Do the math.
Dynamics and keematics are related to change.
Simple observations of our environment show that change is happening around us.
The idea of energy wasn't incorporated into physics until more than one hundred years afterNewton.
These are difficult questions.
There are different forms of energy, and it is difficult to define them.
Energy can come from a number of factors, such as the speed of an object, the storage of energy in springs, and the heat loss to nuclear energy.
The Law ofConservation of Energy is the same truth for all of them.
In a closed system, energy can't just appear out of nowhere, it must always take on another form.
Work is the method of transferring energy from one system to another, force is the agent for change, and energy is the measure of change.
When you lift a book from the floor, you exert a force on it over a distance, and when you push a crate across a floor, you also exert a force on it over a distance.
The newton-meter is now called a joule and abbreviated as J.
The work needed to produce one watt of power takes one joule.
A quantity is work.
There is a positive, negative, and zero work.
60 N*m or 60 J is the figure.
A constant acceleration is delivered on the mass.
The previous formula only works when the work is close to the intended distance.
Positive work increases the speed of an object, while negative work slows it down.
It will be important to note when we relate work with energy.
A warehouse worker pulls on a rope that makes a 30 degree angle with the horizontal to move a crate of goods.
In the previous example, it was assumed that the floor has a coefficient of 0.4.
The angle of 180 degrees is when the parallel but pointing in opposite directions are joined at the tail.
A box slides down a plane.
The work done by gravity is positive since it helps the motion.
A typical trick question is part (b) of this question.
The force applied to the direction of travel does not work.
The work done by friction is negative since it is opposing the motion.
The work done by the force is dependent on force and distance.
The work done by the force is given by the area under the curve of a force versus displacement graph if the force does not remain constant.
The term "under the curve" means between the line itself and zero.
The spring exerts force on the graph.
The area under the curve is the same as the work done.
We have some choices.
You can see this shape by rotating your head, or by looking at the book in 90 degrees.
Similar to the previous chapter, units for work and energy should be limited to kg, m, and s.
This shape is a triangle sitting on top of a rectangular shape.
The area of the triangle and the area of the rectangle are the total area.
Imagine that a steady force is applied to it, causing it to accelerate.
We derived energy from Big Five.
Positive work increases the speed of an object.
We increase its energy.
Making a change in energy is what positive work is about.
The Work-Energy Theorem states that a system gains or loses energy by transferring it through work between the environment and the system.
Doing positive work increases the amount of energy in the air.
The Big Five Equations can be used in some situations.
Problems can be made simpler by skipping the Big Five and using work and energy.
This is because we don't have to worry about the direction of the vectors.
A tennis ball is hit with an initial speed of 50 m/s.
This could be done using the Big Five, but we need to use the concepts of work and energy.
As the ball moves upward, gravity works on it.
The ball's speed is zero, so its energy is also zero.
A pool cue hitting a ball gives it a speed of 2 m/s.
An object has a certain amount of energy due to its motion.
The potential energy comes from the object's position or the system's configuration.
A ball at the edge of a table has energy that can be turned into energy if it falls off.
An arrow in an archer's bow has energy that can be turned into energy if the archer releases it.
Work was done on the object to put it in the given configuration, and since work is the means of transferring energy, these things have stored energy that can be retrieved.
Potential energy can be found in a variety of sources, such as chemical sources, mechanical sources, and objects.
The ability to do work is called energy.
There are different types of potential energy.
The ball would be pulled down to the floor by gravity.
Let's focus on the potential energy.
Someone did 30 J of work to raise the ball from the floor to the table.
By the time the ball reached the floor, it would have acquired a 30 J energy because of the storage of that energy.
The change in the ball's potential energy to move from the floor to the table was +30 J.
Calculating potential energy at a point doesn't tell us much.
We don't care about potential energy when we change it from one point to another.
This will translate into doing work.
The potential energy is expressed in joules.
The work done by gravity as the object is raised does not depend on the path taken by the object.
It wouldn't make a difference if the ball was lifted straight upward or in a curvy path.
Any work done by a nonconservative force is path dependent.
Different paths may require more or less work to get from the initial to final positions, as this is the case for air resistance.
We need a reference level for height in order to use this last equation.
A passenger in an airplane is reading a book.
The floor of the plane may be 9000 m above the ground to someone on the ground.
Values of potential energy are relative.
A stuntwoman scales a rock face.
The potential energy would be turned into energy.
There is an inverse relationship between potential energy and kruic energy.
If no nonconservative forces act on an object or system while it undergoes some change, then mechanical energy is conserved.
Nonconservative forces convert mechanical energy into other energy forms such as heat.
An independent system obeys the law.
Sometimes using energy to solve problems is simpler than using kinematics, since the total mechanical energy remains the same throughout its travel.
A ball of mass 2 kg is pushed off the edge of a table that is above the floor.
Find the speed of the ball as it hits the floor.
Ignoring the air's effect on mechanical energy can be done.
The ball's potential energy decreased while it increased.
One form of energy decreases while the other increases.
A box is projected up a long ramp with an initial speed of 10 m/s.
We can conserve mechanical energy because it is negligible.
All the energy that was added to the universe during the big bang cannot be removed from the universe.
All energy added to any system must come out.
All of the energy used to bring a roller coaster to the top of the first hill is equal to all of the energy needed to get the roller coaster to the starting point.
The total input of energy will always be equal to the total output in this system.
A skydiver jumps from a helicopter that's 3,000 meters above the ground.
Ignoring air resistance can be used to conserve mechanical energy.
Work done by nonconservative forces is placed on the initial energy side because the final energy accounts for both the initial energy and the energy that is dissipated by the object as it overcomes non-conservative forces.
Wile E. Coyote falls off a cliff.
The force of air resistance on the way down has an average strength of 100 N.
Working with energy doesn't take into account vectors.
In order to find out the initial energy, work, or final energy of a problem, we have to solve it backwards with the help ofConservation of Energy.
The problems we have solved in this chapter could have been solved using the kinematics equations andNewton's laws.
In a closed system, changes in energy are not dependent on where you go.
This will allow you to solve many problems that you wouldn't otherwise be able to do.
You don't need to know the mass of the object, you don't need a constant acceleration, and you don't need to know the path the object is travelling.
The easiest approach is energy.
With energy, we can throw out many variables.
A roller coaster rests on top of a hill at an amusement park.
The car rolls down the hill and goes to point B, which is 10 m above the ground, and then goes up the track to point C, which is 20 m above the ground.
Scott and Jean each do 1,000 J of work, but Scott does it in 2 minutes, while Jean does it in 1 minute.
Jean was more powerful because he did it more quickly.
1 W is 1 J/s.
Here in the United States, which still uses older units like inches, feet, yards, miles, ounces, pounds, and so forth, you still hear of power ratings expressed in horsepower.
One horsepower is defined as 746 W.
The conversion will be provided on the test.
The equation only applies to a constant force.
The number is 300 N and 6 m. 90 W. is the ratio of (1,800 J)/(20 s).