Answer:
The rule for kilometers is that every three seconds between a lightning flash and the following thunder gives the distance to the flash in kilometers.
Explanation:
In order to use the rule of thumb to find the speed of sound in meters per second, we need to use some conversion ratios. We know there is 1 mile per every 5 seconds after the lightning is seen. We also know that there are 5280ft in 1 mile and we also know that there are 0.3048m in 1ft. This is enough information to solve this problem. We set our conversion ratios like this:
notice how the ratios were written in such a way that the units got cancelled when calculating them. Notice that in one ratio the miles were on the numerator of the fraction while on the other they were on the denominator, which allows us to cancel them. The same happened with the feet.
The problem asks us to express the answer to one significant figure so the speed of sound rounds to 300m/s.
For the second part of the problem we need to use conversions again. This time we will write our ratios backwards and take into account that there are 1000m to 1 km, so we get:
This means that for every 3.11s there will be a distance of 1km from the place where the lightning stroke. Since this is a rule of thumb, we round to the nearest integer for the calculations to be made easily, so the rule goes like this:
The rule for kilometers is that every three seconds between a lightning flash and the following thunder gives the distance to the flash in kilometers.
Answer:
a) 0.462 m/s^2
b) 31.5 rad/s
c) 381 rad
d) 135m
Explanation:
the linear acceleration is given by:
the angular speed is given by:
to calculate how many radians have the wheel turned we need the apply the following formula:
the distance is given by:
Answer:
4 smaller disks
Explanation:
We are given;
Mass of smaller and larger disks = M
Radius of smaller disk = R
Radius of larger disk = 4R
Formula for moment of inertia about cylinder axis is:
I = ½MR²
Thus;
For small disk, I_small = ½MR²
For large disk, I_large = ½M(2R)² = 2MR²
We are told that moment of inertia of System A consists of two of the larger disks. Thus;
I_A = 2 × I_large = 2 × 2MR²
I_A = 4MR²
We are also told that System B consists of one of the larger disks and a number of the smaller disks. Thus;
I_B = I_large + n(I_small)
Where n is the number of smaller disks.
I_B = 2MR² + n(½MR²)
I_B = MR²(2 + n/2)
We are told that the moment of inertia for system A equals the moment of inertia for system B. Thus;
I_A = I_B
So;
4MR² = MR²(2 + n/2)
MR² will cancel out to give;
4 = 2 + n/2
Multiply through by 2 to give;
8 = 4 + n
n = 8 - 4
n = 4
Answer:
<h2>The answer is planetary motion</h2>
Explanation:
According to Johannes Kepler, the laws governing planetary motion
states that:
1. The orbit of a planet is an ellipse with the Sun at one of the two foci.
2. A line segment joining a planet and the Sun sweeps out equal areas
during equal intervals of time.
3. The square of a planet's orbital period is proportional to the cube of the semi-major of its orbit.
Johannes Kepler was a German astronomer, mathematician, and astrologer
Born: 27 December 1571, Weil der Stadt, Germany
Died: 15 November 1630
Answer:
P.E. = -0.449 J
Explanation:
Potential energy of a charge particle in any electrostatic field is defined as the amount of work done ( in negative ) to bring that charge particle from any position to a new position r.
Now Potential energy is defined by this formula,
P.E. = k q₁ q₂/ r
where P.E. is the potential energy.
k = 1/( 4πε₀) = 8.99 × 10⁹ C²/ ( Nm²)
q₁ = charge of one particle = +1.0μC
q₂ = charge of another particle = -5.0μC
r = distance = 0.1 m
Now , P.E. = 8.99 × 10⁹C²/ ( Nm²) * ( -5.0 × 10⁻⁶ C ) × ( 1 × 10⁻⁶ C ) / 0.1 m
P.E. = -0.449 J
