Everyday forces

Calculate the weight of a rucksack of $5\ \text{kg}$ (take $g = 9,8\ \text{m/s}^2$) and indicate the direction in which this force acts.

A pair of bathroom scales reads $60\ \text{kg}$.

1. a) What do the scales actually measure: mass or weight?
2. b) What is this person's weight in newtons (take $g = 9,8\ \text{m/s}^2$)?
3. c) What would the scales read on the Moon, where gravity is weaker? Reason your answer.

A book of $2\ \text{kg}$ is at rest on a table (take $g = 9,8\ \text{m/s}^2$).

1. a) Draw the forces acting on the book in your exercise book.
2. b) Calculate the weight of the book and the normal reaction force exerted by the table.

You can do it on paper and send a photo with your answer.

A person of $60\ \text{kg}$ is standing on bathroom scales inside a lift (take $g = 10\ \text{m/s}^2$), as shown in the diagram.

1. a) What do the scales read with the lift at rest?
2. b) When the lift accelerates upwards at $2\ \text{m/s}^2$, the normal force is $N = m \cdot (g + a)$: calculate what the scales read in this case.
3. c) Has the person's real weight changed? Explain what has changed.

A person of $60\ \text{kg}$ is standing on bathroom scales inside a lift, and the scales read $660\ \text{N}$ (take $g = 10\ \text{m/s}^2$).

1. a) Calculate the person's real weight.
2. b) Calculate the net force acting on them.
3. c) Deduce the magnitude and direction of the lift's acceleration.

A crate of $20\ \text{kg}$ is pulled along a floor for which the friction force is given by $F_r = \mu \cdot N$, with $\mu = 0,3$ (take $g = 10\ \text{m/s}^2$).

1. a) Calculate the normal force on the crate.
2. b) Calculate the friction force.
3. c) What is the minimum horizontal force that must be applied for the crate to move forward at a constant speed? Justify your answer.

A worker pulls a crate of $10\ \text{kg}$ along a horizontal floor with a force of $60\ \text{N}$, and the friction is $30\ \text{N}$ (take $g = 10\ \text{m/s}^2$). The diagram shows the forces acting on the crate.

1. a) Calculate the weight of the crate and the normal force from the floor.
2. b) Calculate the net horizontal force and the acceleration of the crate.

A student pushes a piece of furniture with increasing force: with $10\ \text{N}$ it does not move, with $20\ \text{N}$ it does not move, with $30\ \text{N}$ it does not move and with $35\ \text{N}$ it starts to slide.

1. a) What was the friction force in each of the first three cases? Justify your answer using Newton's second law.
2. b) What is the maximum value of static friction between the piece of furniture and the floor?
3. c) Once in motion, do you expect the friction to remain the same? Reason your answer using what you know about static and dynamic friction.

A lamp of $3\ \text{kg}$ hangs from the ceiling suspended by a cable (take $g = 9,8\ \text{m/s}^2$).

1. a) What forces act on the lamp and what exerts them?
2. b) Calculate the tension in the cable.

Two teams pull on a rope in opposite directions, each with a force of $350\ \text{N}$, and the rope does not move, as shown in the diagram.

1. a) What is the tension at any point in the rope? (Be careful: it is not the sum of the two forces; explain why.)
2. b) If one of the teams lets go of the rope, what happens to the tension and to the movement of the rope? Explain it.

A locomotive of $2000\ \text{kg}$ pulls two identical rail cars of $2000\ \text{kg}$ each with a force of $6000\ \text{N}$ (consider friction negligible).

1. a) Calculate the acceleration of the system.
2. b) Calculate the tension in the coupling between the locomotive and the first rail car.
3. c) Calculate the tension in the coupling between the two rail cars and explain why it is smaller than the previous one.

When you submerge a beach ball in a swimming pool and let go of it, it shoots upwards. What force, besides weight, acts on the ball while it is submerged? What exerts it and in which direction does it point?

A stone weighs $10\ \text{N}$ in air, and when suspended from a force meter and submerged in water, the device reads $6\ \text{N}$, as shown in the diagram.

1. a) What is the upthrust exerted by the water on the stone?
2. b) In which direction does this force point?
3. c) If the stone were released underwater, would it sink or float? Reason your answer by comparing the weight with the upthrust.

A steel ship of $50000\ \text{kg}$ floats in the harbour, while a steel bolt of $50\ \text{g}$ sinks to the bottom (take $g = 10\ \text{m/s}^2$), as shown in the diagram.

1. a) Calculate the weight of each one (be careful with the mass units).
2. b) If the ship floats in equilibrium, what is the upthrust exerted by the water on it?
3. c) Explaining in terms of the volume of water displaced by each, how is it possible for the ship to generate such a large upthrust while the bolt does not, given that both are made of steel?

A goods lift raises a load of $60\ \text{kg}$ with an acceleration of $2\ \text{m/s}^2$ (take $g = 10\ \text{m/s}^2$).

1. a) Draw the forces acting on the load in your exercise book.
2. b) Calculate its weight.
3. c) Apply Newton's second law to calculate the tension in the cable.

You can do it on paper and send a photo with your answer.

A crate of $5\ \text{kg}$ is on a horizontal floor and is pushed with a horizontal force of $40\ \text{N}$; the friction is $20\ \text{N}$ (take $g = 10\ \text{m/s}^2$).

1. a) Draw the four forces acting on the crate in your exercise book, naming each one and the object that exerts it.
2. b) Calculate the magnitude of all four forces.
3. c) Calculate the net force on the crate and its acceleration.

You can do it on paper and send a photo with your answer.

A student claims: "the normal force is always equal to the weight". To test this, a crate of $10\ \text{kg}$ is placed on the floor and pulled upwards with a rope exerting $30\ \text{N}$, without actually lifting it (take $g = 10\ \text{m/s}^2$).

1. a) Draw the three vertical forces acting on the crate in your exercise book.
2. b) Since the crate is at rest, calculate the magnitude of the normal force.
3. c) Explain why the student's statement is false in general and state in which specific case it would be true.

You can do it on paper and send a photo with your answer.