Exercises: First law: inertia

You are standing on a bus without holding onto anything, and suddenly the driver brakes hard. In which direction does your body lean, forward or backward? Explain using Newton's first law.

Why is it required by law to wear a seat belt even in the back seat of a car? Explain what would happen to your body during sudden, hard braking if you were not wearing one, relating it to inertia.

You place a coin on a piece of cardboard covering the top of a glass and flick the cardboard away suddenly in a horizontal direction, as shown in the figure.

The coin falls into the glass instead of flying off with the cardboard. Explain this trick using Newton's first law.

Complete the sentence with the missing words: "If the net force acting on an object is zero, an object at rest $\dots$ at rest, and a moving object continues to move in a $\dots$ $\dots$ motion at a $\dots$ velocity". Then give an example of each case.

When a car suddenly accelerates from rest, passengers feel their heads jerk backward against the headrest. Does this mean a force is pushing them backward? Explain this using the concept of inertia.

In an ice hockey game, a player hits the puck and it glides almost without slowing down to the far end of the rink. What does Newton's first law say about the motion of the puck while no one touches it? Why does it eventually stop on a real rink?

Sophia is sitting on the sofa at home. Is she at rest or in motion? Answer by choosing two different frames of reference:

1. a) Relative to the walls of her house.
2. b) Relative to the Sun.

What do you conclude about simply stating that "she is still"?

To beat dust out of a rug, it is hung up and hit with a rug beater: the rug moves suddenly and the dust is released. Explain this phenomenon using the inertia of dust.

In shows, you often see the trick of pulling a tablecloth away quickly without knocking over the dishes on top, as shown in the figure.

1. a) Explain why this works using Newton's first law.
2. b) What do you think would happen if you pulled the tablecloth very slowly? Give reasons for your answer.

Mateo is on a train traveling at a constant velocity along a straight track and throws a ball vertically upward, as shown in the figure.

1. a) Does the ball land back in his hand, in front of him, or behind him? Justify your answer.
2. b) Would the answer change if the train were braking at that exact moment? Explain.

On a plane mid-flight, to you your suitcase is stationary in the overhead bin; however, to someone who could see you from the ground, the suitcase is moving at around $900\ \text{km/h}$.

1. a) Who is correct?
2. b) Explain what a frame of reference is and why rest and motion are always described relative to one.

The head of a hammer has loosened from the handle. Your grandfather fixes it by tapping the bottom end of the handle sharply against the ground a few times.

1. a) Explain, using inertia, why the hammer head tightens when doing this.
2. b) How is this trick similar to beating a rug to get rid of dust? Name the underlying concept behind both.

In a bus taking a traffic circle to the left, as shown in the figure (top view), standing passengers lean towards the right.

1. a) Does any force push them to the right?
2. b) Explain this using Newton's first law, considering the direction that each body tends to follow.

A ball rolls across the playground pavement and eventually stops even though no one touches it. A friend says: "This proves that Newton's first law does not hold true in real life." Are they right? Explain which force is involved and what would happen on a perfectly smooth, frictionless surface.

A spacecraft travels through deep space, far from planets and stars, with its engines turned off.

1. a) What does the spacecraft do: does it stop, slow down gradually, or continue at a constant velocity? Justify your answer using Newton's first law.
2. b) Is it necessary to burn fuel to maintain velocity? What about to change it? Explain the difference.

When a wet umbrella is spun rapidly, water droplets fly off in a straight line.

1. a) Explain using inertia why the droplets do not continue spinning with the umbrella once they detach.
2. b) What was holding them attached to the fabric while spinning?

A bottle full of water hangs from a string, with another identical string tied underneath it, as shown in the figure. If you pull the bottom string slowly, the top string breaks; but if you pull it sharply, the bottom string breaks.

1. a) Explain why, when pulling slowly, the top string breaks (think about the forces acting on each string).
2. b) Explain, using the bottle's inertia, why pulling sharply breaks the bottom string.
3. c) Predict what would happen with an almost empty bottle and explain the role of its mass.

Emma has a helium balloon tied with a short string inside her car. Surprisingly, when she brakes, the balloon leans backward, exactly opposite to the passengers.

1. a) Describe what happens to the passengers when braking and explain it using inertia.
2. b) The air inside the car also has inertia: explain what happens to this air when braking and how that explains why the balloon, which is lighter than air, moves backward.

A book is resting on the smooth dashboard of a car (almost frictionless). Describe and explain using Newton's first law what happens to the book in each situation:

1. a) The car suddenly accelerates from rest.
2. b) The car travels at a constant velocity along a straight road.
3. c) The car brakes hard.
4. d) In a real car the dashboard is not so smooth: what role does friction between the book and the dashboard play?

A skateboarder goes down the street and their board hits a small stone: the board stops dead and they fly forward.

1. a) Explain using Newton's first law why they fly forward.
2. b) Relate this accident to the function of a seat belt in a car.
3. c) If, instead of hitting a stone, the skateboard slowed down gradually upon entering grass, would they fly off with as much force? Justify your answer.

Imagine you are traveling in a windowless train car, so well isolated that you cannot hear or feel anything from the outside, and the train travels at a constant velocity along a perfectly straight and smooth track.

1. a) Could you tell, without looking outside, whether the train is stationary or moving? Justify your answer using the first law.
2. b) What if the train accelerated or braked? Describe a simple test you could carry out inside the car to notice it.

Mateo has a plastic cup filled to the brim with water, resting on the car's armrest.

1. a) Explain using inertia why water spills backwards when the car accelerates hard.
2. b) Predict what will happen when taking a fast sharp turn to the right and justify your answer.
3. c) Would the water spill while traveling at $120\ \text{km/h}$ along a straight road if the car moves smoothly with no changes in velocity? Explain the difference.

A tanker truck transports milk with its tank half full. The driver notices that when braking, the liquid cargo "pushes" the truck forward.

1. a) Explain using Newton's first law what the milk inside the tank does when braking.
2. b) Why is it more dangerous to have the tank half full than completely full, with no space for the load to move?
3. c) What precautions should the driver take? Relate them to inertia.

A cyclist traveling at a constant velocity along a straight line drops a wrench from their hand without pushing it. Ignore air resistance.

1. a) As seen by the cyclist, does the wrench land directly below the release point, ahead of it, or behind it? Justify your answer.
2. b) Describe the trajectory seen by a person standing on the sidewalk.
3. c) Explain the difference between both descriptions using frames of reference and inertia.