<h2>
Hello!</h2>
The answer is:
The kinetic energy of the object is equal to 85 J.
<h2>
Why?</h2>
The kinetic energy involves the speed and the mass of an object in motion. We can calculate the following the work needed to speed an object (kinetic energy) using the equation:
Where,
m, is the mas of the object
v, is the speed of the object.
Now, we are given:
So, substituting and calculating the kinetic energy of the object, we have:
We have that the kinetic energy of the object is equal to 85 J.
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Answer:
Explanation:
If the mass of an object is 5 kg, it means that it weighs 5 kg
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Answer:
equation of motion for the mass is x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
Explanation:
Given data
mass = 3 slugs = 3 * 32.14 = 96.52 lbs
constant k = 9 lbs/ft
Beta = 6lbs * s/ft
mass is pulled = 1 ft below
to find out
equation of motion for the mass
solution
we know that The mass is pulled 1 ft below so
we will apply here differential equation of free motion i.e
dx²/dt² + 2 α dx/dt + ω² x =0 ........................1
here 2 α = Beta / mass
so 2 α = 6 / 96.52
α = 0.031
α² = 0.000961 ...............2
and
ω² = k/mass
ω² = 9 /96.52
ω² = 0.093 ..................3
we can say that from equation 2 and 3 that α² - ω² = -0.092239
this is less than zero
so differential equation is
x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
equation of motion for the mass is x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
Answer:
The correct answer is - 63.61 miles/hour.
Explanation:
Meter and miles both are the measuring units of distance and speed units are meter per second and miles per hour. The numerical relation between these two units are as follows:
1 meter per second = 2.24 miles per hour
The car travels 28.4 m/s so in miles per hour it would be:
So, 28.4 meters per second = 28.4 * 2.24 miles per hour
28.4 meters per second = 63.61 miles per hour.
Thus, the correct answer is - 63.61 miles per hour.
Answer: 18.27°
Explanation:
Given
Index of refraction of blue light, n(b) = 1.64
Wavelength of blue light, λ(b) = 440 nm
Index of refraction of red light, n(r) = 1.595
Wavelength of red light, λ(r) = 670 nm
Angle of incident, θ = 30°
Angle of refraction of red light is
θ(r) = sin^-1 [(n(a)* sin θ) / n(r)], where n(a) = index of refraction of air = 1
So that,
θ(r) = sin^-1 [(1 * sin 30) / 1.595]
θ(r) = sin^-1 (0.5 / 1.595)
θ(r) = sin^-1 0.3135
θ(r) = 18.27°
