Exercises: Everyday applications: weight, normal force, friction, and road safety

A lamp is sitting still on a nightstand and does not fall to the floor, as shown in the diagram.

The Earth pulls down on it with its weight: what other force acts on the lamp, what exerts it, and in what direction does it point?

Name two everyday situations where friction helps us (without it we could not do something) and explain each one briefly.

Name two everyday situations where friction is a hindrance (wastes energy, wears out parts, or causes heating) and explain how it is usually reduced in each case.

Explain why it is so easy to slip when walking on an icy sidewalk. What does friction have to do with it? Why is salt or sand spread over the ice?

Explain the purpose of a bicycle helmet by considering what would happen to your head in a fall, with and without a helmet. What is the advantage of making the impact last a little longer?

Car tires have a tread pattern and must be changed when they are "bald." Explain the purpose of this tread pattern and the danger of driving with bald tires, especially on wet roads.

You hold a bag with $2\ \text{kg}$ of oranges in your open hand, keeping it still, as shown in the diagram. Take $g \approx 10\ \text{m/s}^2$.

1. a) How much does the bag weigh?
2. b) With what force does your hand push upward? Justify your answer considering that the bag is not accelerating.

Complete the sentence and give an example from everyday life: 'The friction force between two surfaces in contact always opposes the relative $\dots$ between them, or the tendency to $\dots$'.

A $60\ \text{kg}$ washing machine is sitting still on the kitchen floor. Take $g \approx 10\ \text{m/s}^2$.

1. a) Calculate its weight.
2. b) What is the magnitude of the normal force exerted by the floor on it? Justify your answer.
3. c) Weight and the normal force are equal and opposite forces, but they do NOT form an action-reaction pair: explain why (hint: notice which body each acts upon).

To drag the couch across the living room, you have to push hard at first, but once it moves, it slides with less effort.

1. a) Explain the difference between static friction and kinetic friction.
2. b) What would happen to the required force if you removed the cushions and emptied the drawers beforehand? Justify your answer.

Braking on a bicycle over a patch of ice is very dangerous.

1. a) Explain what happens to the wheel and to friction if you brake hard on ice.
2. b) Predict why it is better to brake gently and mainly use the rear brake in that situation.

Order these situations from shortest to longest stopping distance and justify the order considering the speed and the available friction:

1. a) A car traveling at $50\ \text{km/h}$ on a dry road surface.
2. b) The same car traveling at $50\ \text{km/h}$ on a wet road surface.
3. c) The same car traveling at $100\ \text{km/h}$ on a dry road surface.

Dragging a heavy dresser across a carpet is much harder than across a polished marble floor.

1. a) Explain why, referencing the friction between the surfaces in contact.
2. b) Name a situation where it is desirable to have high friction and another where low friction is desirable.

Skiers wax the base of their skis before a competition.

1. a) What do they achieve by doing this? Relate it to friction.
2. b) Give another example of a sport or machine in which wax, oil, or another lubricant is used, and explain its function.

In a crash, the driver's head tends to keep moving forward (first law). The airbag inflates in a fraction of a second to slow it down.

1. a) Why is stopping the head with the airbag less harmful than against the steering wheel?
2. b) Relate your answer to Newton's second law: what happens to the force if the braking action is spread over a longer time?

A motorcycle helmet has a thick layer of foam inside that deforms when it receives an impact.

1. a) Explain the advantage of the foam deforming instead of being completely rigid.
2. b) Why is it recommended to replace the helmet after a hard impact even if it appears intact on the outside?

A book is sitting still on a table, as shown in the diagram.

1. a) Name the two forces acting on the book, who exerts each one, and in what direction.
2. b) Explain why these two forces do not form an action-reaction pair.
3. c) Indicate the true reaction force to the weight of the book (hint: what does the book attract?) and the true reaction force to the normal force (hint: what force does the book exert on the table?).

You pull a $10\ \text{kg}$ luggage cart across the airport floor with a horizontal force of $30\ \text{N}$, as shown in the diagram, and the cart moves forward at a constant speed.

1. a) What is the net force acting on the cart? What is the value of friction then?
2. b) Suddenly you pull with $50\ \text{N}$ (and friction remains the same): calculate the acceleration of the cart.
3. c) Newton's first law states that without forces an object would keep moving: why do you have to keep pulling to maintain a constant speed? There is no contradiction: explain why.

Two identical cars (same mass) travel, one at $50\ \text{km/h}$ and the other at $100\ \text{km/h}$, and both brake at the same time with the same braking force.

1. a) Using Newton's second law, explain why both decelerate equally.
2. b) Reason which of the two will need more time to stop and, therefore, more meters.
3. c) Using this idea, explain why speed limits in residential areas are $30\ \text{km/h}$ or $50\ \text{km/h}$ rather than $120\ \text{km/h}$.

In driver's ed courses, it is recommended to double or triple the safe following distance when it rains.

1. a) Explain what happens to the friction between the tire and the road surface when wet (water acts as a "lubricant").
2. b) Relate this lower friction to the maximum available braking force and, using Newton's second law, to the deceleration the car can achieve.
3. c) Conclude: why must you drive slower in the rain even if the car and brakes are exactly the same?

Analyze a head-on collision at $50\ \text{km/h}$ using Newton's laws:

1. a) Explain, using Newton's first law, what happens to the body of an unbelted passenger at the moment of impact.
2. b) Explain two things the seat belt does to protect them: holding them in place and distributing the force across strong parts of the body.
3. c) The airbag extends the duration of the head's deceleration: using Newton's second law, explain why this reduces the force experienced by the head.

A broken-down car needs to be pushed to move it off the road. It takes a huge effort to get it moving, but once it rolls, it keeps moving with a gentle push.

1. a) Explain the first part using inertia and static friction.
2. b) Explain the second part using kinetic friction and Newton's first law.
3. c) If you stopped pushing on flat asphalt, would the car stop instantly? Justify your answer.

Sections of road with loose gravel are particularly dangerous on curves.

1. a) Explain, using Newton's first law, what a car tends to do when approaching a curve.
2. b) What force actually enables the car to turn? What happens if this force is small because of loose gravel?
3. c) Relate the above to "loose gravel" warning signs and to the recommendation of reducing speed before the curve, not during it.

Modern cars are designed with "crumple zones": the bodywork crumples in a controlled way during a crash.

1. a) At first glance, a rigid non-deformable car seems better: explain why it would actually be worse for the passengers.
2. b) Relate the deformation to the duration of the crash deceleration and, using Newton's second law, to the force felt by the passengers.
3. c) How is this design similar to the airbag and the helmet foam?

Topic challenge. Design a road safety expert report analyzing braking and inertia in vehicles.

Phase 1. Experimentation: Push a small box across a table always using the same tension from a rubber band. Measure the braking distance $d$ with a ruler ($\pm 0.1\text{ cm}$), varying the mass: empty ($m$), with coins ($2m$), and with triple the mass ($3m$). Carry out three trials per mass, calculate the mean with its uncertainty, and construct a data table and a graph of $d$ versus $m$.

Phase 2. Newtonian analysis: Explain the motion using Newton's 1st Law (inertia). Apply the 2nd Law ($F = m \times a$) to deduce the net braking force and identify the action-reaction pair (3rd Law) between the object and the surface, sketching the weight, normal force, and friction.

Phase 3. Road safety application: Check the official NHTSA website for factors that alter stopping distance. Write a reasoned proposal with three recommendations for drivers, using the physics studied and the NHTSA data to justify the danger of overloading and tire wear, and discuss whether your experimental data are enough to explain the danger of overloading.

Assessment criteria:

• Rigor in data collection, uncertainty handling, and plotting of the data table and graph.

• Scientific accuracy when applying Newton's three laws and the forces involved.

• Quality of the road safety proposal supported by experimental data and NHTSA findings.