The fundamental principle of dynamics
An empty lorry and the same lorry loaded to the brim pull away with the engine delivering the same force. The empty one shoots off; the loaded one takes much longer to pick up speed. The law that explains this is the same one that lets us calculate the acceleration of a rocket or a shopping trolley: the fundamental principle of dynamics.
F = m · a: the fundamental principle
If you push an empty supermarket trolley, you notice it speeds up straight away; if you push the trolley with the same force when it is full to the top, you can hardly get it to accelerate. How are the force you apply, the mass of the object and the change in velocity you achieve related mathematically?
Calculate the net force required for a toy cart of $2\ \text{kg}$ to accelerate at $3\ \text{m/s}^2$.
Calculate the net force required for a toy cart of $2\ \text{kg}$ to accelerate at $3\ \text{m/s}^2$.
A net force of $20\ \text{N}$ acts on a box of $5\ \text{kg}$. What acceleration does the box acquire?
A net force of $20\ \text{N}$ acts on a box of $5\ \text{kg}$. What acceleration does the box acquire?
The newton: the unit of force
We measure mass in kilograms and acceleration in metres per second squared, but how do we define precisely the unit we use to measure the push or pull on a body?
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 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.
The same force of $50\ \text{N}$ is applied first to a ball of $0,5\ \text{kg}$ and then to a medicine ball of $5\ \text{kg}$, as shown in the figure. Calculate the…
The same force of $50\ \text{N}$ is applied first to a ball of $0,5\ \text{kg}$ and then to a medicine ball of $5\ \text{kg}$, as shown in the figure.
Calculate the acceleration of each one and explain which accelerates more and why.
The net force: you have to add up all the forces
Almost no body receives just one force. To apply $F = m \cdot a$ you first need to calculate the net force: the result of adding, as vectors, all the forces acting on the body (push, friction, tension...).
A person pushes a toolbox of $8\ \text{kg}$ with a force of $60\ \text{N}$, and the friction with the ground is $20\ \text{N}$. a) Calculate the net force on the box. b)…
A person pushes a toolbox of $8\ \text{kg}$ with a force of $60\ \text{N}$, and the friction with the ground is $20\ \text{N}$.
- a) Calculate the net force on the box.
- b) Calculate its acceleration.
A car of $1000\ \text{kg}$ brakes with a net force of $5000\ \text{N}$, as shown in the figure. a) Calculate its acceleration and interpret the sign of the result. b) If…
A car of $1000\ \text{kg}$ brakes with a net force of $5000\ \text{N}$, as shown in the figure.
- a) Calculate its acceleration and interpret the sign of the result.
- b) If it was travelling at $20\ \text{m/s}$, calculate how long it takes to come to a stop (use $v = v_0 + a \cdot t$).
To pull a sledge of $30\ \text{kg}$ across the snow, a force of $90\ \text{N}$ is applied to it and the friction is $30\ \text{N}$. A student calculates the acceleration…
To pull a sledge of $30\ \text{kg}$ across the snow, a force of $90\ \text{N}$ is applied to it and the friction is $30\ \text{N}$. A student calculates the acceleration like this: $a = 90 / 30 = 3\ \text{m/s}^2$.
- a) Identify the mistake made.
- b) Calculate the correct acceleration of the sledge.
- c) Calculate the total force with which it would need to be pulled for the acceleration to actually be $3\ \text{m/s}^2$.
Mass and acceleration: an inverse relationship
A full supermarket trolley has a mass of $15\ \text{kg}$ and a net force of $30\ \text{N}$ is applied to it. a) Calculate its acceleration. b) If it starts from rest,…
A full supermarket trolley has a mass of $15\ \text{kg}$ and a net force of $30\ \text{N}$ is applied to it.
- a) Calculate its acceleration.
- b) If it starts from rest, what speed does it reach after $3\ \text{s}$?
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…
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 $8000\ \text{kg}$.
- a) Calculate the acceleration of each lorry.
- b) Calculate the time each lorry takes to reach $20\ \text{m/s}$.
- c) Using these numbers, explain why a loaded lorry needs more distance to join a motorway.