Mechanical energy: kinetic and potential
A skater going down a ramp, a stone at the top of a cliff, a drone flying at top speed and at a great height at the same time. All of them have mechanical energy, but not of the same kind: some have it because they are moving, others because they are up high, and some for both reasons.
Kinetic energy: the energy of motion
If a tennis ball rolls slowly and hits your leg you barely notice it, but if it hits you after a powerful serve it hurts a lot, and if what is rolling slowly is a lorry the consequences are devastating: which variables determine the ability of a moving body to produce effects around it?
Kinetic energy is calculated as $E_c = \frac{1}{2} \cdot m \cdot v^2$. A toy car of $2\ \text{kg}$ moves at $3\ \text{m/s}$. Calculate its kinetic energy.
Kinetic energy is calculated as $E_c = \frac{1}{2} \cdot m \cdot v^2$. A toy car of $2\ \text{kg}$ moves at $3\ \text{m/s}$. Calculate its kinetic energy.
A football of $0,5\ \text{kg}$ is kicked off at $20\ \text{m/s}$. What kinetic energy does it have?
A football of $0,5\ \text{kg}$ is kicked off at $20\ \text{m/s}$. What kinetic energy does it have?
A car of $1000\ \text{kg}$ travels at $72\ \text{km/h}$. a) Express its speed in $\text{m/s}$. b) Calculate its kinetic energy.
A car of $1000\ \text{kg}$ travels at $72\ \text{km/h}$.
- a) Express its speed in $\text{m/s}$.
- b) Calculate its kinetic energy.
Gravitational potential energy
A brick resting on the ground poses no danger, but that same brick placed on the window ledge of a fifth-floor flat stores an obvious destructive capacity if it is dropped: what form of energy does an object store simply by being raised up, and which quantities does it depend on?
Potential energy is calculated as $E_p = m \cdot g \cdot h$. A book of $1\ \text{kg}$ is on a shelf $5\ \text{m}$ off the ground (take $g = 10\ \text{m/s}^2$), as shown…
Potential energy is calculated as $E_p = m \cdot g \cdot h$. A book of $1\ \text{kg}$ is on a shelf $5\ \text{m}$ off the ground (take $g = 10\ \text{m/s}^2$), as shown in the diagram.
Calculate its potential energy.
A plant pot of $2\ \text{kg}$ is on a balcony railing, $1,5\ \text{m}$ above the ground (take $g = 9,8\ \text{m/s}^2$). Calculate its potential energy.
A plant pot of $2\ \text{kg}$ is on a balcony railing, $1,5\ \text{m}$ above the ground (take $g = 9,8\ \text{m/s}^2$). Calculate its potential energy.
A painting of $4\ \text{kg}$ is hung first $2\ \text{m}$ off the floor and then raised to $6\ \text{m}$ (take $g = 10\ \text{m/s}^2$), as shown in the diagram. a)…
A painting of $4\ \text{kg}$ is hung first $2\ \text{m}$ off the floor and then raised to $6\ \text{m}$ (take $g = 10\ \text{m/s}^2$), as shown in the diagram.
- a) Calculate its potential energy in each position.
- b) What is the relationship between height and potential energy? Express it using the numbers above.
Mechanical energy: the sum of the two
A roller-coaster car almost comes to a complete stop at the highest peak, plunges down at full speed and slows down again as it climbs the next hill: which overall quantity combines the car's height and speed at each instant?
State what type of mechanical energy each body has and explain why: a) A car driving along a motorway. b) A rock on the edge of a cliff. c) An aeroplane in mid-flight.
State what type of mechanical energy each body has and explain why:
- a) A car driving along a motorway.
- b) A rock on the edge of a cliff.
- c) An aeroplane in mid-flight.
Which of these two bodies has more mechanical energy (kinetic plus potential)? Calculate it for each one (take $g = 10\ \text{m/s}^2$): a) A crane of $5\ \text{kg}$…
Which of these two bodies has more mechanical energy (kinetic plus potential)? Calculate it for each one (take $g = 10\ \text{m/s}^2$):
- a) A crane of $5\ \text{kg}$ flying at $10\ \text{m/s}$ at a height of $100\ \text{m}$.
- b) A stone of $10\ \text{kg}$ at rest at a height of $300\ \text{m}$.
The diagram summarises the situation:
A drone of $2\ \text{kg}$ flies at a height of $20\ \text{m}$ with a speed of $10\ \text{m/s}$ (take $g = 10\ \text{m/s}^2$), as shown in the diagram. a) Calculate its…
A drone of $2\ \text{kg}$ flies at a height of $20\ \text{m}$ with a speed of $10\ \text{m/s}$ (take $g = 10\ \text{m/s}^2$), as shown in the diagram.
- a) Calculate its kinetic energy.
- b) Calculate its potential energy.
- c) What is its total mechanical energy?
- d) If it stops in mid-air while maintaining its height, what happens to each of those energies?
Watch out: doubling the speed does not double the energy
A trolley of $2\ \text{kg}$ has a kinetic energy of $100\ \text{J}$. At what speed is it moving? First rearrange the kinetic energy formula for speed.
A trolley of $2\ \text{kg}$ has a kinetic energy of $100\ \text{J}$. At what speed is it moving? First rearrange the kinetic energy formula for speed.
A remote-controlled car travels at $4\ \text{m/s}$ and its kinetic energy is $40\ \text{J}$. a) What is its mass? b) What kinetic energy would it have if it travelled at…
A remote-controlled car travels at $4\ \text{m/s}$ and its kinetic energy is $40\ \text{J}$.
- a) What is its mass?
- b) What kinetic energy would it have if it travelled at $8\ \text{m/s}$?
A passenger car of $1000\ \text{kg}$ travels at $30\ \text{m/s}$ and a lorry of $4000\ \text{kg}$ travels at $15\ \text{m/s}$. a) Calculate the kinetic energy of each…
A passenger car of $1000\ \text{kg}$ travels at $30\ \text{m/s}$ and a lorry of $4000\ \text{kg}$ travels at $15\ \text{m/s}$.
- a) Calculate the kinetic energy of each vehicle.
- b) Which one has more kinetic energy? Did you expect that result?
- c) Explain, using the formula, why speed "weighs" more than mass in kinetic energy.