Balanced forces

Mateo pushes a box to the right with $3\ \text{N}$ and Sophia 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?

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.

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?

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.

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.

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

1. a) Think of a backpack hanging from a coat hook 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.

Liam and Olivia 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.

Two people push a shopping cart 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 cart.
2. b) Does the cart move forward?
3. c) What would friction need to be for the cart to be in equilibrium?

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 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 swing hangs from two identical chains. The swing weighs $40\ \text{N}$ and Mateo, 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?

A store 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: $6\ \text{N}$ toward goal A and $10\ \text{N}$ toward goal B.

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