The fundamental principle of dynamics

Calculate the net force required for a toy cart of $2\ \text{kg}$ to accelerate at $3\ \text{m/s}^2$.

A scooter together with its rider accelerates at $2\ \text{m/s}^2$ when a net force of $100\ \text{N}$ acts on the combination. Calculate the total mass.

A net force of $20\ \text{N}$ acts on a box of $5\ \text{kg}$. What acceleration does the box acquire?

Using Newton's second law, show that $1\ \text{N}$ is equivalent to $1\ \text{kg} \cdot \text{m/s}^2$ and give a simple numerical example to illustrate it.

A person pushes a toolbox of $8\ \text{kg}$ with a force of $60\ \text{N}$, and the friction with the ground is $20\ \text{N}$.

1. a) Calculate the net force on the box.
2. b) Calculate its acceleration.

Three forces act on a crate of $10\ \text{kg}$ along the same line: $50\ \text{N}$ to the right, $30\ \text{N}$ to the right and $20\ \text{N}$ to the left.

1. a) Calculate the net force.
2. b) Calculate the acceleration of the crate.
3. c) What additional force would need to be applied so that the crate moves at constant velocity? Reason your answer.

A worker pushes a trolley of $20\ \text{kg}$ with a force of $100\ \text{N}$ and the friction is $20\ \text{N}$.

1. a) Calculate the acceleration of the cart.
2. b) If the worker doubles their push to $200\ \text{N}$ and the friction does not change, does the acceleration double as well? Calculate it and explain why this happens.

An aeroplane flies in a straight line at a constant velocity of $250\ \text{m/s}$. What is the net force on the aeroplane? What is its acceleration? Relate this to Newton's second law of motion.

A sledge slides along horizontal ice and we stop pushing it. A classmate claims: "since there is no longer any force pushing it, it will stop straight away".

1. a) According to Newton's second law, how would the sledge move if friction were exactly zero? What would the net force on it be then?
2. b) On real ice the sledge eventually comes to a stop: which force is responsible and in which direction does it act?
3. c) Explain why the classmate's statement confuses "there is no applied force" with "there is no net force".

A motorcycle with its rider has a mass of $200\ \text{kg}$ and travels at $72\ \text{km/h}$.

1. a) Express the speed in $\text{m/s}$.
2. b) Calculate the net braking force required to stop in $4\ \text{s}$.

In a laboratory, the acceleration of a trolley is measured when different forces are applied to it: with $2\ \text{N}$ it accelerates at $0,5\ \text{m/s}^2$; with $4\ \text{N}$, at $1\ \text{m/s}^2$; and with $6\ \text{N}$, at $1,5\ \text{m/s}^2$.

1. a) Plot force against acceleration in your exercise book and describe the graph you obtain.
2. b) Deduce the mass of the trolley from the data.
3. c) Predict the acceleration of the trolley if a force of $10\ \text{N}$ were applied to it.

Two lorries with identical engines, producing the same net force of $8000\ \text{N}$, start from rest: one is empty, with a mass of $4000\ \text{kg}$, and the other is loaded, with a mass of $8000\ \text{kg}$.

1. a) Calculate the acceleration of each lorry.
2. b) Calculate the time each lorry takes to reach $20\ \text{m/s}$.
3. c) Using these numbers, explain why a loaded lorry needs more distance to join a motorway.