The change in internal energy of the gas is
.
In fact, the 1st law of thermodynamics states that the change in internal energy of a system is equal to the amount of heat given to the system (Q) plus the work done on the system (W):
In this example, no work is done on the bottle so W=0, while the heat given to the system is
, so the change in internal energy of the gas is
Ek = (m*V^2) / 2 where m is mass and V is speed, then we can take this equation and manipulate it a little to isolate the speed.
Ek = mv^2 / 2 — multiply both sides by 2
2Ek = mv^2 — divide both sides by m
2Ek / m = V^2 — switch sides
V^2 = 2Ek / m — plug in values
V^2 = 2*30J / 34kg
V^2 = 60J/34kg
V^2 = 1.76 m/s — sqrt of both sides
V = sqrt(1.76)
V = 1.32m/s (roughly)
A) Net force in component form: 
B) Magnitude of the net force: 316.2, direction: 
Explanation:
A)
The three forces given in this problem are:
The three forces are given in component form, where the components with unit vector i is the component along the x-direction, while the components with unit vector j is the component along the y-direction.
In order to find the net force in component form, we just need to add the components of the three forces along each direction. Therefore:
- Along the x-direction:
- Along the y-direction:
So, the net force in component form is
B)
The magnitude of a vector F is given by Pythagorean's theorem:
where in this problem,
is the x-component
is the y-component
Substituting,
The direction instead is given by
where the negative sign means the direction is below the positive x-axis.
Learn more about vector addition:
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F = 2820.1 N
Explanation:
Let the (+)x-axis be up along the slope. The component of the weight of the crate along the slope is -mgsin15° (pointing down the slope). The force that keeps the crate from sliding is F. Therefore, we can write Newton's 2nd law along the x-axis as
Fnet = ma = 0 (a = 0 no sliding)
= F - mgsin15°
= 0
or
F = mgsin15°
= (120 kg)(9.8 m/s^2)sin15°
= 2820.1 N
The answer is C because <span>this movement is caused by the heat in Earth and creates </span>convection currents. <span>Convection currents in the asthenosphere cause movement of Earth's tectonic plates. </span>
