Answer:
The answer to your question is
Explanation:
Data
mass = 0.5kg
T1 = 35
T2 = ?
Q = - 6.3 x 10⁴ J = - 63000 J
Cp = 4184 J / kg°C
Formula
Q = mCp(T2 - T1)
T2 = T1 + Q/mCp
Substitution
T2 = 35 - 63000/(0.5 x 4184)
T2 = 35 - 63000/2092
T2 = 35 - 30.1
T2 = 4.9 °C
The frequency of the wheel is given by:

where N is the number of revolutions and t is the time taken. By using N=100 and t=10 s, we find the frequency of the wheel:

And now we can find the angular speed of the wheel, which is related to the frequency by:
To develop this problem it will be necessary to apply the concepts related to the frequency of a spring mass system, for which it is necessary that its mathematical function is described as

Here,
k = Spring constant
m = Mass
Our values are given as,


Rearranging to find the spring constant we have that,




Therefore the spring constant is 1.38N/m
Answer:
The kinetic energy K of the moving charge is K = 2kQ²/3d = 2Q²/(4πε)3d = Q²/6πεd
Explanation:
The potential energy due to two charges q₁ and q₂ at a distance d from each other is given by U = kq₁q₂/r.
Now, for the two charges q₁ = q₂ = Q separated by a distance d, the initial potential energy is U₁ = kQ²/d. The initial kinetic energy of the system K₁ = 0 since there is no motion of the charges initially. When the moving charge is at a distance of r = 3d, the potential energy of the system is U₂ = kQ²/3d and the kinetic energy is K₂.
From the law of conservation of energy, U₁ + K₁ = U₂ + K₂
So, kQ²/d + 0 = kQ²/3d + K
K₂ = kQ²/d - kQ²/3d = 2kQ²/3d
So, the kinetic energy K₂ of the moving charge is K₂ = 2kQ²/3d = 2Q²/(4πε)3d = Q²/6πεd
Answer:
4.32
Explanation:
The centripetal acceleration of any object is given as
A(cr) = v²/r, where
A(c) = the centripetal acceleration
v = the linear acceleration
r = the given radius, 1.9 m
Since we are not given directly the centripetal acceleration, we'd be using the value of acceleration due to gravity, 9.8. This means that
9.8 = v²/1.9
v² = 1.9 * 9.8
v² = 18.62
v = √18.62
v = 4.32 m/s
This means that, the minimum speed the cup must have so as not to get wet or any spill is 4.32 m/s