Kinetic energy and potential energy

Kinetic energy is calculated as $E_c = \frac{1}{2} \cdot m \cdot v^2$. A volleyball of $0,3\ \text{kg}$ reaches the player's hands at $24\ \text{m/s}$. Calculate its kinetic energy.

Your classmate calculates the kinetic energy of a car of $1000\ \text{kg}$ travelling at $90\ \text{km/h}$ by substituting $v = 90$ into the formula, and obtains $4050000\ \text{J}$.

1. a) What mistake has your classmate made?
2. b) Calculate the kinetic energy correctly yourself, first converting the speed to $\text{m/s}$.
3. c) Explain why it is compulsory to always work in SI units.

Potential energy is calculated as $E_p = m \cdot g \cdot h$. A lamp of $3\ \text{kg}$ hangs from the ceiling $2,5\ \text{m}$ above the floor (take $g = 9,8\ \text{m/s}^2$). Calculate its potential energy.

An astronaut lifts a rock of $20\ \text{kg}$ to a height of $1,5\ \text{m}$, first on Earth ($g = 9,8\ \text{m/s}^2$) and then on Mars ($g = 3,7\ \text{m/s}^2$).

1. a) Calculate the potential energy gained by the rock on each planet.
2. b) Where is it "harder" to lift it? Justify your answer using your results.
3. c) Has the mass of the rock changed upon travelling to Mars? What about its weight?

Complete the sentence with the missing words: "The mechanical energy of an object is the $\dots$ of its $\dots$ energy and its $\dots$ energy". Then give an example of an object that has both types of energy at the same time.

A peregrine falcon of $1\ \text{kg}$ dives at $60\ \text{m/s}$ when it is at a height of $500\ \text{m}$, while a pigeon of $0,4\ \text{kg}$ flies at $20\ \text{m/s}$ at a height of $100\ \text{m}$ (take $g = 10\ \text{m/s}^2$), as shown in the figure.

1. a) Calculate the kinetic energy and potential energy of each bird.
2. b) Which bird has more total mechanical energy?

A microlight aircraft of $300\ \text{kg}$ flies at a height of $500\ \text{m}$ with a speed of $40\ \text{m/s}$ (take $g = 10\ \text{m/s}^2$).

1. a) Calculate its kinetic energy.
2. b) Calculate its potential energy.
3. c) What is its total mechanical energy?
4. d) If it descends to $200\ \text{m}$ while maintaining the same speed, how much mechanical energy does it lose? Where do you think that energy goes?

A skier of $80\ \text{kg}$ travels down a slope at $12\ \text{m/s}$. What is his kinetic energy?

A cat of $4\ \text{kg}$ is sitting on top of a wall and its potential energy relative to the ground is $196\ \text{J}$ (take $g = 9,8\ \text{m/s}^2$). How high is the wall?

A car of $1200\ \text{kg}$ travels at $20\ \text{m/s}$.

1. a) Calculate its kinetic energy.
2. b) A motorbike and its rider have a combined mass of $300\ \text{kg}$ and have the same kinetic energy: at what speed is it travelling?
3. c) Explain, using the formula, why having a quarter of the mass corresponds to exactly double the speed.

A football of $0,45\ \text{kg}$ bounces off at $40\ \text{m/s}$.

1. a) Calculate its kinetic energy.
2. b) At what speed would an athlete of $80\ \text{kg}$ have to run to have the same kinetic energy? Rearrange the formula for speed first.

A rescue helicopter of $3000\ \text{kg}$ ascends from a height of $100\ \text{m}$ to $300\ \text{m}$ while maintaining a constant speed of $20\ \text{m/s}$ (take $g = 10\ \text{m/s}^2$).

1. a) Calculate its kinetic energy: does it change during the ascent?
2. b) Calculate the potential energy it gains.
3. c) How does its mechanical energy change? Where does this energy come from?