Exercises: Equilibrium of forces

Complete the sentence: "We say that an object is in equilibrium when all the forces acting on it $\dots$ each other, so that the net force is $\dots$."

Seán pushes a box to the right with $3\ \text{N}$ and Aoife also pushes it to the right with $4\ \text{N}$, as shown in the figure.

1. a) Calculate the net force on the box.
2. b) In which direction will the box move?

Two children push a table in opposite directions: one exerts $10\ \text{N}$ to the right and the other, $6\ \text{N}$ to the left, as shown in the figure.

1. a) What is the value of the net force on the table?
2. b) Which way does the table move?

In a game of tug-of-war, Aoife's team pulls the rope with $500\ \text{N}$ to the left and Seán's team pulls with $500\ \text{N}$ to the right, as shown in the figure.

1. a) What is the net force on the rope?
2. b) Who is winning the game at that moment?

A lamp hangs from the ceiling without moving, as shown in the figure.

1. a) Name the two forces acting on it and state which direction each one points in.
2. b) Is the lamp in equilibrium? Justify your answer.

A book is resting on a table, as shown in the figure.

Are any forces acting on it? State the forces present and explain why the book does not move.

Complete the sentence: "When two forces have the same line of action and opposite directions, the net force is the $\dots$ of their values and points in the direction of the $\dots$ force." Then give an example with numbers.

Two children push a toy train. If both push in the same direction, one with $2\ \text{N}$ and the other with $5\ \text{N}$, what is the net force? What if the second child pushes in the opposite direction with their $5\ \text{N}$?

Three forces act on a box along the same line: $2\ \text{N}$ and $3\ \text{N}$ to the right, and $5\ \text{N}$ to the left.

1. a) Calculate the net force on the box.
2. b) Will the box move? Justify your answer.

Two dogs pull on a rope toy: the larger dog pulls to the left with $45\ \text{N}$ and the smaller one to the right with $40\ \text{N}$.

1. a) Calculate the net force on the toy and state which direction it moves in.
2. b) What extra force would the smaller dog need to exert for the toy to be in equilibrium?

A flowerpot weighs $20\ \text{N}$ and hangs stationary from a hook.

1. a) What force does the hook exert on the flowerpot?
2. b) If the same flowerpot hung from two hooks sharing the weight equally, what force would each hook exert?

A crate is pushed to the right with $8\ \text{N}$.

1. a) What force would need to be added for the crate to be in equilibrium?
2. b) What if, in addition to the $8\ \text{N}$, there were another $2\ \text{N}$ pushing in the same direction?

Bruno and Claudia push a box in the same direction, with $15\ \text{N}$ and $20\ \text{N}$, while friction with the floor is $30\ \text{N}$ in the opposite direction.

1. a) Calculate the net force on the box.
2. b) Does the box move? Justify your answer.

A drone hovers stationary in the air, neither rising nor falling. Its weight is $50\ \text{N}$, as shown in the figure.

1. a) What is the upward force exerted by its propellers?
2. b) To start ascending, must this force be greater than, less than, or equal to the weight? Justify your answer.

A swing hangs from two identical chains. The swing weighs $40\ \text{N}$ and Cian, sitting still, weighs $360\ \text{N}$, as shown in the figure.

1. a) What total upward force do the chains exert?
2. b) If the load is shared equally, what force does each chain support?

Two people push a shopping trolley in the same direction, with $60\ \text{N}$ and $40\ \text{N}$, and friction is $70\ \text{N}$.

1. a) Calculate the net force on the trolley.
2. b) Does the trolley move forward?
3. c) What would friction need to be for the trolley to be in equilibrium?

In the tug-of-war final, three students participate per team. The red team pulls to the left with forces of $150\ \text{N}$, $140\ \text{N}$, and $160\ \text{N}$; the blue team pulls to the right with $145\ \text{N}$, $155\ \text{N}$, and $140\ \text{N}$.

1. a) Calculate the total force of each team.
2. b) What is the value of the net force and in which direction does it point?
3. c) What additional force does the losing team need to balance the rope?

You push a wardrobe to the right with $12\ \text{N}$ and it does not move.

1. a) What is the net force on the wardrobe?
2. b) What is the value of the friction force and in which direction does it point?
3. c) If you push with $30\ \text{N}$ and it still does not move, what is the value of friction now? Explain what is special about friction based on these results.

A shop wants to hang a lamp weighing $120\ \text{N}$ from the ceiling. It has cables that can support a maximum of $50\ \text{N}$ each.

1. a) If the lamp were hung from a single cable, would it hold? Justify your answer.
2. b) What about with two cables sharing the weight equally? Justify your answer with calculations.
3. c) What is the minimum number of cables needed?

On an air-hockey table, a puck lying on the line joining the two goals (at opposite ends of the table) receives two pushes at the same time: $6\ \text{N}$ towards goal A and $10\ \text{N}$ towards goal B.

1. a) Calculate the net force acting on the disc.
2. b) What third force, in magnitude and direction, would need to be applied so that the disc remains in equilibrium?
3. c) If the disc was stationary and we apply that third force, will it move?

Read this statement: "If the net force on an object is zero, no forces are acting on it."

1. a) Think of a rucksack hanging from a coat peg and explain why the statement is false.
2. b) Write down the corrected statement.
3. c) Give another everyday example of an object in equilibrium on which at least two forces are acting.

A crane holds a beam weighing $800\ \text{N}$ hanging and stationary, as shown in the figure.

1. a) What force does the crane cable exert on the beam?
2. b) To start lowering the beam slowly, must the cable pull with a force greater than or less than the weight? Give reasons for your answer.
3. c) If, while lowering, the cable pulls with $750\ \text{N}$, what is the net force on the beam and in which direction does it point?

Cian and Aoife push a sofa to the right with $60\ \text{N}$ and $50\ \text{N}$, and the friction with the floor is $100\ \text{N}$.

1. a) Calculate the net force on the sofa. Does it move?
2. b) For the sofa to be in equilibrium, what force would their father need to exert and in which direction?
3. c) If instead their father pushes in the same direction as them with $40\ \text{N}$, what is the net force?

The awning of a market stall weighs $80\ \text{N}$ and hangs from two identical ropes that share the weight equally.

1. a) What force does each rope support?
2. b) The ropes can support a maximum of $50\ \text{N}$: are they suitable for the awning?
3. c) The seller adds a tarpaulin and the total weight becomes $120\ \text{N}$. If he wants each rope to continue supporting the same amount, how many ropes does he need at a minimum? Justify your answer with calculations.