Answer:
Wavelength = 0.7083 meters
Explanation:
Given the following data;
Speed of wave = 340 m/s
Frequency = 480 Hz
To find how long is the sound wave, we would determine its wavelength;
Mathematically, the wavelength of a waveform is given by the formula;
Wavelength = velocity/frequency
Wavelength = 340/480
Wavelength = 0.7083 meters
Answer:
0.3 m
Explanation:
Initially, the package has both gravitational potential energy and kinetic energy. The spring has elastic energy. After the package is brought to rest, all the energy is stored in the spring.
Initial energy = final energy
mgh + ½ mv² + ½ kx₁² = ½ kx₂²
Given:
m = 50 kg
g = 9.8 m/s²
h = 8 sin 20º m
v = 2 m/s
k = 30000 N/m
x₁ = 0.05 m
(50)(9.8)(8 sin 20) + ½ (50)(2)² + ½ (30000)(0.05)² = ½ (30000)x₂²
x₂ ≈ 0.314 m
So the spring is compressed 0.314 m from it's natural length. However, we're asked to find the additional deformation from the original 50mm.
x₂ − x₁
0.314 m − 0.05 m
0.264 m
Rounding to 1 sig-fig, the spring is compressed an additional 0.3 meters.
So, the work was done by that hot air-balloon is <u>30,000 J or 30 kJ</u>.
<h3>Introduction</h3>
Hi ! In this question, I will help you. <u>Work is the amount of force exerted to cause an object to move a certain distance from its starting point</u>. In physics, the amount of work will be proportional to the increase in force and increase in displacement. Amount of work can be calculated by this equation :

With the following condition :
- W = work (J)
- F = force (N)
- s = shift or displacement (m)
Now, the s (displacement) can be written as ∆h (altitude change) because the object move to vertical line. The formula can also be changed to:

With the following condition :
- W = work (J)
- F = force (N)
= change of altitude (m)
If an object has mass, then the object will also be affected by gravity. Always remember that F = m × g. So that :


With the following condition :
- W = work (J)
- m = mass of the object (kg)
- g = acceleration of the gravity (m/s²)
= change of altitude (m)
<h3>Problem Solving</h3>
We know that :
- F = force = 100 N
= change of altitude 300 m
What was asked :
Step by step :



<h3>Conclusion</h3>
So, the work was done by that hot air-balloon is 30,000 J or 30 kJ.
<h3>See More :</h3>
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50N is your force and the acceleration is -9.8m/s^2 due to gravity.
So, you just plug that in.

BUT you know that mass cannot be negative, so you just disregard the negative sign and the mass of the rock is 5.102 grams.
Answer:
Time period, T = 403.78 years
Explanation:
It is given that,
Orbital distance, 
Mass of the Earth, 
Mass of the planet, 
Let T is the orbital period of this planet. The Kepler's third law of motion gives the relation between the orbital period and the orbital distance.



or
T = 403.78 years
So, the orbital period of this planet is 404 years. Hence, this is the required solution.