Which forces act on a body · printable packet

Draw one object alone with an arrow for every force on it, each exerted by something; at rest, the forces balance.

Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.

1. What you will learn

By the end of this lesson you will be able to list every force on an object, name what exerts each one, and find an unknown force by balancing.

2. What you already have

You know that a force is a push or a pull, measured in newtons, and that balanced forces leave an object's motion unchanged. You have seen friction slow things down. This lesson shows how to list every force on one object and find their sizes.

3. Words for this lesson

4. Every force has a source

A free-body diagram shows one object by itself, with an arrow for each force acting on it. Each arrow must be exerted by some other object:

When an object is at rest, the forces balance: the upward forces equal the downward ones, and the leftward equal the rightward.

Term	What it means
Force	A push or a pull, measured in newtons, N.
Weight	Earth's pull on an object, $W = mg$, with $g = 9.8$ N/kg.
Normal force	A surface's push, straight out from the surface.
Tension	The pull of a rope, string or cable along its length.
Friction	A surface's resistance to sliding, along the surface.
Free-body diagram	A drawing of one object with an arrow for every force on it.

Another way: picture

Picture a backpack hanging from a hook on the classroom wall. Earth pulls it down with its weight. The strap pulls it up with a tension. Nothing else touches it. The backpack is still, so the strap's pull exactly balances the weight.

Another way: steps

Choose one object and draw it alone.
Draw its weight straight down.
Find everything touching it and draw the force each exerts.
Label each arrow with its source.
If the object is at rest, make the forces balance.

5. One object at a time

A free-body diagram is about a single object. Draw it as a box or a dot, alone on the page, and draw only the forces acting on it. Forces that it exerts on other things belong on their diagrams, not this one.

This sounds simple, but it is where most force mistakes begin. A book on a table pushes down on the table, but that push acts on the table. On the book's diagram you draw only the table pushing up and Earth pulling down.

6. Weight

Earth pulls on every object near it. This pull is the object's weight, and it points straight down, toward Earth's center. Its size is the mass times $9.8$ newtons per kilogram, $W = mg$.

A $2$ kg bag of flour has a weight of $19.6$ N. Weight is the only everyday force that acts without touching; every other force in this lesson needs contact.

7. Normal forces

A surface pushes back on anything pressing on it. The push points straight out from the surface, which is why it is called the normal force; normal means at right angles.

A table's normal force on a resting book equals the book's weight. If you press down on the book, the table pushes up harder. Surfaces adjust their push to whatever is needed, up to the point where they break.

8. Tension

A rope, string, chain or cable can only pull, never push. The pull acts along the rope, away from the object it is attached to, and is called tension.

A lamp hanging from a ceiling cable is pulled up by the tension and down by its weight. At rest, the two balance. If two cables share the load equally, each carries half the weight.

9. Friction

When one surface slides, or tries to slide, over another, friction acts along the surfaces to resist the sliding. Push a heavy box across the floor and friction pushes back against you.

If you push the box at a steady speed, friction exactly balances your push. If you push harder, the forces no longer balance and the box speeds up, the subject of the lessons ahead.

10. The method, step by step, and how to check it

Checking an answer. Every arrow must name an object that exerts it. An object at rest must have balanced forces. A force the object exerts on something else must not appear on its own diagram.

11. Why each step is allowed

Forces come from interactions between objects. Earth interacts with everything through gravity; other forces come from touching. So listing the objects that touch something, plus Earth, lists every force on it.

When forces balance, an object's motion does not change: it stays at rest or keeps moving steadily. That is why a resting object must have forces that add to zero, and why the size of an unknown force can be found by balancing.

12. No force of motion

A soccer ball rolling across a field after a kick has no forward force pushing it. The kick's force stopped the instant the foot left the ball. What keeps the ball rolling is simply that nothing has stopped it yet.

On the ball's diagram, there is its weight, the ground's normal force, and a small friction and air drag slowing it. No arrow points forward, because nothing is pushing it forward.

13. Forces in balance

A book at rest on a table, a lamp hanging still, a car parked on level ground: each has forces that balance. The upward forces add to the same size as the downward ones.

Balanced forces do not mean no forces. The book has two forces on it, weight and normal force, equal in size and opposite in direction. Together they add to zero, so the book stays put.

14. Stacked objects

When boxes are stacked, each box's diagram shows the box above pressing down on it and the box below or the floor pushing up. The floor must hold up the whole stack, so it pushes with the total weight.

Warehouses and grocery stores limit how high boxes may be stacked, because the bottom box must withstand the weight of everything above it without crushing.

15. Forces in buildings

Every floor of a building pushes up on the people and furniture on it, and the columns and walls push up on each floor. Engineers draw free-body diagrams for beams and columns to make sure every force is balanced.

A column near the bottom of a skyscraper carries the weight of every floor above it, which is why lower columns are thicker. The same balancing that works for a book on a table keeps the tallest buildings standing.

16. Common slips

Three errors are common. Drawing a force the object exerts, instead of one exerted on it, puts the arrow on the wrong diagram. Forgetting the weight leaves a normal force with nothing to balance.

The third is drawing a force of motion pointing the way the object moves. Moving objects need no forward force to keep going; only a change in motion needs an unbalanced force.

17. Mass and weight

Mass, in kilograms, is how much matter an object has. Weight, in newtons, is the force of Earth's pull on it. On the Moon a bag of flour has the same mass but only about a sixth of the weight.

Everyday talk often mixes them up, saying a person weighs sixty kilograms. In physics, a sixty-kilogram person has a weight of five hundred eighty-eight newtons.

18. Drawing arrows to scale

In a careful free-body diagram, the length of each arrow shows the size of the force. A book's weight and the table's push are drawn the same length, pointing in opposite directions.

When forces are unequal, the arrows show it at a glance. A crate pushed harder than friction resists gets a longer push arrow than friction arrow, a picture of the unbalanced force that will speed it up.

19. Forces come in pairs

Whenever one object pushes or pulls on another, the second object pushes or pulls back just as hard in the opposite direction. The book presses down on the table, and the table presses up on the book. Earth pulls the book down, and the book pulls Earth up by exactly the same amount.

The two forces of a pair always act on different objects, so they never appear on the same free-body diagram. That is why the book's diagram shows the table pushing up, but not the book pushing down: that second force belongs on the table's diagram.

20. Checking a diagram by asking who

A quick test for any free-body diagram is to point at each arrow and ask who is doing that. For the weight, the answer is Earth. For a normal force, it is the surface. For a tension, the rope. If you cannot name the object, the arrow does not belong.

This simple question catches invented forces, such as a force of motion or a force of the throw, which have no object behind them. It also reminds you to look for every object touching the one you are drawing, so that no real force is left out.

21. In the world: truck scales on the interstate

Along American interstates, weigh stations check that trucks are not overloaded. A truck drives onto a scale, and the scale measures how hard each axle pushes down, which equals the upward normal force the scale supplies.

Federal rules limit a loaded tractor-trailer to about thirty-six thousand kilograms, a weight of over three hundred fifty thousand newtons, shared among its axles. Too much weight on one axle damages roads and bridges. Inspectors add up the axle forces, exactly as a free-body diagram adds the upward forces, to check that they balance the truck's total weight and that no single axle carries too much.

22. In the world: elevator cables

Every elevator hangs from steel cables. When the car is stopped at a floor, the cables' tension balances the weight of the car and its passengers. A car with a mass of one thousand kilograms, carrying ten people of seventy kilograms, has a total weight of about sixteen thousand seven hundred newtons.

Building codes require several cables, each able to hold the full load on its own, so one broken cable cannot drop the car. Inspectors check the cables regularly. The free-body diagram is simple, tension up and weight down, but getting it right is what keeps millions of elevator riders safe every day.

23. There is no force of motion

It is natural to think a moving object must have a force pushing it along, and to draw an arrow in the direction of motion. But a ball rolling after a kick has nothing pushing it forward. Every force needs an object that exerts it, and nothing is touching the ball from behind.

A related error is to leave out forces from surfaces, thinking a table just sits there. The table pushes up on the book with exactly enough force to hold it; without that push, the book would fall.

24. A lamp on a cable

25. A box with a push

26. A rolling ball

27. Your turn: a $5$ kg bag of rice rests on a shelf. How hard does the shelf push up on it?

28. Guided practice

A $3$ kg book rests on a level table. With $g = 9.8$ N/kg, how hard does the table push up on the book, in N?

29. Guided practice

Complete the worked solution: a $1.5$ kg box sits on top of a $5$ kg box on the floor. With $g = 9.8$ N/kg, find the top box's weight in N, the bottom box's weight in N, and the floor's upward push on the bottom box in N.

30. Guided practice

31. Practice

A $8$ kg box sits on the floor. With $g = 9.8$ N/kg, fill in its weight in N, the floor's push in N while someone presses down on the box with $16$ N, and the floor's push in N while someone instead pulls up on it with $40$ N.

32. Practice

A $15$ kg box rests on a level floor, and a person presses straight down on it with a force $P$, in newtons. With $g = 9.8$ N/kg, write the floor's upward push, in N, as a function of $P$.

33. Practice

A $12$ kg store sign hangs at rest from two vertical ropes that pull equally. With $g = 9.8$ N/kg, what is the tension in each rope, in N?

34. Somewhere new

a Toyota Prius has a mass of about $1400$ kg and is parked on level ground. If its weight is shared equally by its four tires, how hard does the ground push up on each tire, in N? Use $g = 9.8$ N/kg.

35. Lesson test

Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.

36. Test question

A $10$ kg box rests on a level floor, and a person presses straight down on it with a force $P$, in newtons. With $g = 9.8$ N/kg, write the floor's upward push, in N, as a function of $P$.

37. What you can do now

You can draw a free-body diagram. Explain to someone why a soccer ball rolling after a kick has no forward force on it.

Working for the steps left to you

	force
weight (N)
floor's push with the press (N)
floor's push with the pull (N)

27. Your turn: a $5$ kg bag of rice rests on a shelf. How hard does the shelf push up on it?, step 3