Answer:
19.5°
Explanation:
The energy of the mass must be conserved. The energy is given by:
1) 
where m is the mass, v is the velocity and h is the hight of the mass.
Let the height at the lowest point of the be h=0, the energy of the mass will be:
2) 
The energy when the mass comes to a stop will be:
3) 
Setting equations 2 and 3 equal and solving for height h will give:
4) 
The angle ∅ of the string with the vertical with the mass at the highest point will be given by:
5) 
where l is the lenght of the string.
Combining equations 4 and 5 and solving for ∅:
6) 
The phenomenon which is responsible for this effect is called diffraction.
Diffraction is the ability of a wave to propagate when it meets an obstacle or a slit. When the wave encounters the obstacle or the slit, it 'bends' around it and it continues propagate beyond it. A classical example of this phenomenon is when a sound wave propagates through a wall where there is a small aperture (as in the example of this problem)
Answer:
(D) 4
Explanation:
The percentage error in each of the contributors to the calculation is 1%. The maximum error in the calculation is approximately the sum of the errors of each contributor, multiplied by the number of times it is a factor in the calculation.
density = mass/volume
density = mass/(π(radius^2)(length))
So, mass and length are each a factor once, and radius is a factor twice. Then the total percentage error is approximately 1% +1% +2×1% = 4%.
_____
If you look at the maximum and minimum density, you find they are ...
{0.0611718, 0.0662668} g/(mm²·cm)
The ratio of the maximum value to the mean of these values is about 1.03998. So, the maximum is 3.998% higher than the "nominal" density.
The error is about 4%.
_____
<em>Additional comment</em>
If you work through the details of the math, you will see that the above-described sum of error percentages is <em>just an approximation</em>. If you need a more exact error estimate, it is best to work with the ranges of the numbers involved, and/or their distributions.
Using numbers with uniformly distributed errors will give different results than with normally distributed errors. When such distributions are involved, you need to carefully define what you mean by a maximum error. (By definition, normal distributions extend to infinity in both directions.) While the central limit theorem tends to apply, the actual shape of the error distribution may not be precisely normal.
Answer:
The resulting magnetic field is 5.021 x 10⁻⁵ T
Explanation:
Given;
current in the lightening bolt, I = 11800 A
distance from the bolt, r = 47 m
permeability of free space, μ₀ = 1.25664 × 10⁻⁶ T· m/A
Assume lightening bolt as long straight conductor, then the resulting magnetic field will be calculated as follows;
where;
B is the resulting magnetic field
I is the current in the bolt
r is the distance from the bolt
Substitute the given values and calculate B
Thus, the resulting magnetic field is 5.021 x 10⁻⁵ T
First put the speed in m/s. 120km/h = 33.33m/s. Now the position function is the integral of velocity, and velocity is in turn the integral of acceleration. The velocity is:
Now we integrate this expression to get the position. The constant of integration will be the distance the truck travels.
Here we set the distance, 35m as negative because I assumed the stopping point of the truck is the origin. Putting t=0 shows it starts at -35m.
Now solve the following equation for the time, t using the quadratic equation:
and choose the value t=1.149s
