The final volume of the gas is 3 L
Explanation:
We can solve this problem by applying Boyle's law, which states that:
"For a gas kept at constant temperature, the pressure of the gas is inversely proportional to its volume"
Mathematically:
where
P is the pressure of the gas
V is its volume
The equation can also be rewritten as
For the sample of helium in this problem, we have:
Solving the equation, we can find , the final volume of the gas:
Learn more about ideal gases:
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Answer:
F = 0.768 i ^ - 0.576 j ^ + 0.24 k ^
the correct answer is "b"
Explanation:
The magnetic force is
F = i l x B
The bold are vectors, in this case they give us the direction of the current and the magnetic field, for which we can solve as a determinant
resolver
F = i ^ (4 12 - 0) + j ^ (0- 3 12) + k ^ (3 5 - 0)
F = i (48 i ^ - 36 j ^ + 15 k⁾
in this case i is the value of the current flowing through the cable
i = 16 mA = 0.016 A
F = 0.768 i ^ - 0.576 j ^ + 0.24 k ^
When reviewing the different answers, the correct answer is "b"
(a) See graph in attachment
The appropriate graph to draw in this part is a graph of velocity vs time.
In this problem, we have a horse that accelerates from 0 m/s to 15 m/s in 10 s.
Assuming the acceleration of the horse is uniform, it means that the velocity (y-coordinate of the graph) must increase linearly with the time: therefore, the velocity-time graph will appear as a straight line, having the final point at
t = 10 s
v = 15 m/s
(b)
The average acceleration of the horse can be calculated as:
where
v is the final velocity
u is the initial velocity
t is the time interval
In this problem,
u = 0
v = 15 m/s
t = 10 s
Substituting,
(c) 75 m
For a uniformly accelerated motion, the distance travelled can be calculated by using the suvat equation:
where
s is the distance travelled
u is the initial velocity
t is the time interval
a is the acceleration
In this problem,
u = 0
t = 10 s
Substituting,
(d) See attached graphs
In a uniformly accelerated motion:
- The distance travelled (x) follows the equation mentioned in part c,
So, we see that this has the form of a parabola: therefore, the graph x vs t will represents a parabola.
- The acceleration is constant during the motion, and its value is
(calculated in part b)
therefore, the graph acceleration vs time will show a flat line at a constant value of 1.5 m/s^2.
(a)
For an electromagnetic wave incident on a surface, the radiation pressure is given by (assuming all the radiation is absorbed)
where
I is the intensity
c is the speed of light
In this problem, ; substituting this value, we find the radiation pressure:
the force exerted on the Earth depends on the surface considered. Assuming that the sunlight hits half of the Earth's surface (the half illuminated by the Sun), we have to consider the area of a hemisphere, which is
where
is the Earth's radius. Substituting,
And so the force exerted by the sunlight is
(b)
The gravitational force exerted by the Sun on the Earth is
where
G is the gravitational constant
is the Sun's mass
is the Earth's mass
is the distance between the Sun and the Earth
Substituting,
And so, the radiation pressure force on Earth as a fraction of the sun's gravitational force on Earth is