Newton's second law: force and acceleration

A remote-controlled car has a mass of $2\ \text{kg}$. What resultant force is required for it to accelerate at $3\ \text{m/s}^2$? Apply $F = m \cdot a$.

The newton is the SI unit of force: $1\ \text{N}$ is the force that must be applied to a mass of $1\ \text{kg}$ so that it accelerates at $1\ \text{m/s}^2$. From this definition, calculate:

1. a) How many newtons are needed for a mass of $1\ \text{kg}$ to accelerate at $3\ \text{m/s}^2$.
2. b) How many newtons are needed for a mass of $3\ \text{kg}$ to accelerate at $1\ \text{m/s}^2$.

A delivery person pushes a $5\ \text{kg}$ parcel along a smooth floor with a resultant force of $20\ \text{N}$. What acceleration does the parcel acquire? Rearrange $a$ from the expression $F = m \cdot a$ first and then calculate.

A rucksack has a mass of $4\ \text{kg}$. Calculate its weight on Earth using $P = m \cdot g$ with $g \approx 10\ \text{m/s}^2$ to get a whole number.

A watermelon has a mass of $2\ \text{kg}$. Calculate its weight on Earth taking the exact value $g = 9,8\ \text{m/s}^2$.

Calculate the weight of a person of $50\ \text{kg}$:

1. a) Taking $g \approx 10\ \text{m/s}^2$.
2. b) Taking the more exact value $g = 9,8\ \text{m/s}^2$.
3. c) What is the difference, in newtons, between the two results?

You drag a $6\ \text{kg}$ box along the floor by pushing with $40\ \text{N}$, while friction pulls it backwards with $10\ \text{N}$, as shown in the figure.

1. a) What is the resultant force on the box?
2. b) Calculate its acceleration.

A $1200\ \text{kg}$ car accelerates from $0$ to $30\ \text{m/s}$ in $6\ \text{s}$. Its engine can exert a force of $7000\ \text{N}$, as shown in the figure.

1. a) Calculate the acceleration of the car.
2. b) Calculate the resultant force required to achieve that acceleration.
3. c) The difference between the engine force and the resultant force is the total friction (air resistance and tyres): what is its value?

A $30\ \text{kg}$ wardrobe is resting on the floor. You push horizontally with $100\ \text{N}$ and it does not move. The figure shows the forces acting on the wardrobe in this situation and in part b.

1. a) If it does not move, what is the resultant force acting on it? What is the friction force then?
2. b) Now you push with $150\ \text{N}$ and the wardrobe starts to slide; while moving, the friction is $120\ \text{N}$. Calculate its initial acceleration.
3. c) Explain why at first it did not move even though you were pushing.

You push an empty shopping trolley and a fully loaded one with the same force, as shown in the figure.

Which of the two accelerates more? Explain using Newton's second law, without performing any calculations.

The same force of $12\ \text{N}$ pushes, separately, a $2\ \text{kg}$ chair and a $6\ \text{kg}$ table across a smooth floor.

1. a) Calculate the acceleration of each piece of furniture.
2. b) How many times greater is the acceleration of the chair compared to the table? Relate this to the ratio of their masses.

On a frozen lake, with negligible friction, you push two blocks of ice, one of $10\ \text{kg}$ and another of $30\ \text{kg}$, with the same force of $60\ \text{N}$ for $2\ \text{s}$ each, as shown in the figure. Both start from rest.

1. a) Calculate the acceleration of each block.
2. b) Calculate the velocity reached by each block after those $2\ \text{s}$.
3. c) Explain why the lighter block ends up moving faster even though the force was the same.