Answer:
v = 719.2 m / s and a = 83.33 m / s²
Explanation:
This is a rocket propulsion system where the system is made up of the rocket plus the ejected mass, where the final velocity is
v - v₀ = 
ln (M₀ / M)
where v₀ is the initial velocity, v_{e} the velocity of the gases with respect to the rocket and M₀ and M the initial and final masses of the rocket
In this case, if fuel burns at 75 kg / s, we can calculate the fuel burned for the 10 s
m_fuel = 75 10
m_fuel = 750 kg
As the rocket initially had a mass of 3000 kg including 1000 kg of fuel, there are still 250 kg, so the mass of the rocket minus the fuel burned is
M = 3000 -750 = 2250 kg
let's calculate
v - 0 = 2500 ln (3000/2250)
v = 719.2 m / s
To calculate the acceleration, let's use the concept of the rocket thrust, which is the force of the gases on it. In the case of the rocket, it is
Push = v_{e} dM / dt
let's calculate
Push = 2500 75
Push = 187500 N
If we use Newton's second law
F = m a
a = F / m
let's calculate
a = 187500/2250
a = 83.33 m / s²
Answer:
h = 51020.40 meters
Explanation:
Speed of the rifle, v = 1000 m/s
Let h is the height gained by the bullet. It can be calculated using the conservation of energy as :
h = 51020.40 meters
So, the bullet will get up to a height of 51020.40 meters. Hence, this is the required solution.
<h2>The increase in length = 1.87 x 10⁻²</h2>
Explanation:
When copper rod is heated , its length increases
The increase in length can be found by the relation
L = L₀ ( 1 + α ΔT )
here L is the increased length and L₀ is the original length
α is the coefficient of linear expansion and ΔT is the increase in temperature .
The increase in length = L - L₀ = L₀ x α ΔT
Substituting all these value
Increase in length = 27.5 x 1.7 x 10⁻⁵ x 35.9
= 1.87 x 10⁻² m
Nichrome wire. That's the stuff that toasters are made from. The resistance is pretty high, considering the diameter. 1 meter is at about the same guage as that listed below for copper is about 96 ohms.
Most of the time you are trying to use wire with the least resistance.
A meter of copper has a listed resistance of 0.024 ohms / meter. The wire is a 19 guage wire which makes it pretty thin.
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I'm not sure what you are asking. If want the resistance of something in terms of what would increase the resistance of the same material for both calculations then
Rule 1: It you decrease the wire diameter, you increase the resistance
Rule 2: If you increase the length of the wire, you increase the resistance.
Both rules assume you are using something like copper.
