12 Questions
What is the formula to calculate mechanical energy?
Em = Ek + Ep
In the context of mechanical energy, what does 'mgh' represent?
Potential energy
What is the total mechanical energy of a 300 g clam carried by a seagull flying horizontally at 8.00 m/s, when the clam is 30.0 m above the ground?
144.8 J
What is the gravitational potential energy of a 55.0 kg high-jump athlete at the top of the leap, moving at 8.33 m/s with a total mechanical energy of 3.00 x 10^3 J?
2750 J
When a construction worker drops a 2.00 kg hammer from 50.0 m above the ground with a total mechanical energy of 1.88 x 10^3 J, what is the kinetic energy of the hammer?
235 J
What is used to calculate the speed of a 10.0 kg water balloon just before it hits the ground when dropped from a height of 12.0 m?
$\sqrt{2gh}$
What is the total mechanical energy of a 55.0 kg high-jump athlete moving at 8.33 m/s at the top of the leap?
3.00 x 10^3 J
In the Law of Conservation of Energy, what is equal to 0.5mv^2?
Kinetic energy
What is the kinetic energy of a 2.00 kg hammer dropped from a roof when it is 50.0 m above the ground?
2.00 x 10^3 J
If a seagull flying at 8.00 m/s carries a clam with a mass of 300 g, what is the kinetic energy of the clam?
20 J
When a water balloon of 10.0 kg is dropped from a height of 12.0 m, what is its gravitational potential energy just before hitting the ground?
1176 J
If a construction worker drops a hammer from a roof and it has a total mechanical energy of 1.88 x 10^3 J, what is the potential energy of the hammer at that moment?
-1500 J
Study Notes
Mechanical Energy
- Mechanical energy (Em) is the sum of kinetic energy (Ek) and potential energy (Ep): Em = Ek + Ep
- The formula for mechanical energy: Em = (0.5mv2) + (mgh)
Examples of Mechanical Energy Calculations
- A seagull flying horizontally at 8.00 m/s carries a clam with a mass of 300 g in its beak. The total mechanical energy of the clam when the seagull is 30.0 m above the ground can be calculated.
- A 55.0 kg high-jump athlete has a total mechanical energy of 3.00 × 10³ J and is moving at 8.33 m/s. The gravitational potential energy of the athlete can be calculated.
- A 2.00 kg hammer is dropped from a roof and has a total mechanical energy of 1.88 × 10³ J when it is 50.0 m above the ground. The kinetic energy of the hammer can be calculated.
Law of Conservation of Energy
- The Law of Conservation of Energy states that the total amount of energy in a given situation remains constant.
- Energy can be converted from one form to another, but the total amount remains the same: Ep = Ek, and mgh = 0.5mv2
Example of Applying the Law of Conservation of Energy
- A 10.0 kg water balloon is dropped from a height of 12.0 m. The speed of the balloon just before it hits the ground can be calculated using the Law of Conservation of Energy.
This quiz covers the definition of mechanical energy and how to calculate it using the formula Em = Ek + Ep. Two examples are provided to practice applying the formula to real-life situations involving moving objects at various heights.
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