Exercises: Everyday forces: weight, normal reaction force, friction, tension and upthrust

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 cup is resting on the kitchen worktop. Which object exerts the normal force on the cup? In which direction does it point? Why do you think it is called a "normal" force?

A rugby player slides across the grass after a tackle. Draw the player sliding to the right in your exercise book and represent the friction force on him: in which direction does it point and why?

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

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.

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 plant pot is resting on a windowsill, at rest. List the forces acting on it, stating which object exerts each one, and draw the force diagram in your exercise book.

You can do it on paper and send a photo with 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 crate of $20\ \text{kg}$ is pulled along a floor for which the friction force is given by $F_r = \mu \times N$, 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.

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 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 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 $N = m \times (g + a)$: calculate what the scales read in this case.
3. c) Has the person's real weight changed? Explain what has changed.

An astronaut has a mass of $80\ \text{kg}$.

1. a) Calculate their weight on Earth ($g = 9.8\ \text{m/s}^2$).
2. b) Calculate their weight on the Moon, where $g = 1.6\ \text{m/s}^2$.
3. c) Has their mass changed upon going to the Moon? What about their weight? Explain the difference between the two concepts.

On a book resting on a table, the weight and the normal force act, having the same magnitude and opposite directions. A student claims: "since they are equal and opposite, they are an action-reaction pair". Explain why the student is mistaken, stating which object each of these forces acts upon and what the true "partner" force of each one is according to Newton's third law.

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 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 lorry travels along a motorway at constant speed and its engine exerts a force of $2000\ \text{N}$.

1. a) What is the total friction force (air resistance and tyres) under these conditions? Justify your answer using Newton's second law.
2. b) If the engine increases its force to $2600\ \text{N}$ and the friction remains the same, calculate the net force and explain what happens to the lorry's speed.
3. c) Air resistance increases with speed: using this information, explain why the lorry cannot exceed a certain maximum speed no matter how hard the accelerator is pressed.

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 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.

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 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 parachutist of $70\ \text{kg}$ descends with an open parachute at a constant speed of $5\ \text{m/s}$ (take $g = 10\ \text{m/s}^2$).

1. a) What is the magnitude of the air resistance force on the parachute? Justify your answer using Newton's second law.
2. b) Before the parachute opened, the parachutist was also falling at a constant speed, of $50\ \text{m/s}$. Was the air resistance then greater, smaller or equal to that with the open parachute? Reason your answer.
3. c) Explain what happens to the net force at the instant the parachute opens and why the parachutist slows down until reaching a new constant speed.

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.

Unit challenge. How do forces interact in everyday real situations? Design a technical report investigating the forces acting on a canned food or plastic container in your own home.

1. Equilibrium and buoyant force: Measure the mass of the empty container and its volume ($m \pm 0.001\text{ kg}$). Submerge it closed (with air inside) and fully in water, tethered to the bottom with a string; numerically determine the buoyant force $\vec{E}$, the tension $\vec{T}$, and the weight $\vec{P}$, drawing the vector diagram at equilibrium to scale.

2. Dynamic friction: Add 4 different masses of rice or water to the container. Pull it horizontally at constant velocity along a table using a previously calibrated elastic band. Record the value of the normal force $\vec{N}$ and the frictional force $\vec{F}_r$ in a table, including their associated uncertainties.

3. Processing and prediction: Plot $F_r$ versus $N$, deduce the coefficient of friction $\mu$ from the slope, and apply Newton's second law ($\sum \vec{F} = m \vec{a}$) to calculate the acceleration of the container if a constant horizontal force of $2.0\text{ N}$ were applied to it with one of the loads from part 2 (state which), first checking whether this force exceeds friction.

4. Report: Write a reasoned proposal summarizing the vector analysis, the graph, and your conclusions.

Evaluation criteria:

• Precise identification, vector resolution, and calculation of $\vec{P}$, $\vec{N}$, $\vec{F}_r$, $\vec{T}$, and $\vec{E}$.

• Experimental quality in taking measurements, estimating uncertainties, and graphical plotting.

• Correct application of the fundamental principle of dynamics ($\sum \vec{F} = m \vec{a}$).

• Structure, consistency, and scientific justification of the final report.