Answer:
The temperature raise is = 0.14 [C]
Explanation:
In order to find the temperature difference we must use the following equation:
But first we need to find the original volume V:
When the volume is increased the diameter will be larger:
D1 = 0.125[m] + 0.0002[m] = 0.1252[m]
Therefore the new radius will be:
r1=0.0626[m]
The new volume is:
Replacing all the calculated values in the equation:
Answer:
T = 8.19 s
, = 23 m / s
Explanation:
In the simple harmonic motion the equation that describes them is
y = A cos wt
Acceleration can be found by derivatives
a = d²y / dt²
v = dy / dt = - Aw sin wt
a= d²y / dt² = - A w² cos wt
For maximum acceleration cosWT = + -1
= -A w2
w = RA (/ A)
w = RA (1.8 9.8 / 30.0)
w = 0.767 rad / s
The angular velocity is related to the frequency
w = 2π f
f = 1 / T
w = 2π / T
T = 2π / w
T = 2π / 0.767
T = 8.19 s
For maximum speed the sin wt = + -1
= A w
= 30.0 0.767
= 23 m / s
The moment of inertia for rolling motion is
I = Mr²
The linear velocity is v = 2 m/s. The rotational velocity is
ω = 2/r
The total KE (kinetic energy) is
KE = (1/2)Mv² + (1/2) I ω²
= (1/2)(M)(4) + (1/2)(Mr²)(4/r²)
= 2M + 2M
= 4M
Answer: 4M
Answer:
Explanation:
Given
Paddle wheel work is
Heat transfer from the tank is
From the first law of thermodynamics
Change in the internal energy of the system is equal to the difference of heat and work .
Therefore, the change in internal energy is