Given Information"
Kinectic energy = 6.5 MeV
magnetic field = B = 1.9 T
Period = T = 1 ms
Required Information"
Diameter = d = ?
Answer:
d = 38.6 cm
f = 1000
Explanation:
(a) What is the diameter of the largest orbit, just before the protons exit the cyclotron?
The radius and hence the diameter of the largest orbit can be found by using
r = mv
/|q|B
Where q = 1.60x10⁻¹⁹ C and m = 1.67x10⁻²⁷ kg and v is the speed of the particle which can be found by using
v = √2K
/m
Where K is the kinetic energy in Joules.
1 eV is equal to 1.60x10⁻¹⁹ J
K = 6.5x10⁶*1.60x10⁻¹⁹ = 1.04x10⁻¹² J
v = √2*1.04x10⁻¹²
/1.67x10⁻²⁷
v = 35.29x10⁶ m/s
r = 1.67x10⁻²⁷*35.29x10⁶
/1.60x10⁻¹⁹*1.9
r = 0.193 m
d = 2r
d = 2*0.193 = 0.386
or d = 38.6 cm
(b) A proton exits the cyclotron 1.0 ms after starting its spiral trajectory in the center of the cyclotron. How many orbits does the proton complete during this 1.0 ms?
The period T and frequency (number of rotations per second) are related as
f = 1/T
f = 1/0.001
f = 1000
The complete question is;
James Joule (after whom the unit of energy is named) claimed that the water at the bottom of Niagara Falls should be warmer than the water at the top, 51 m above the bottom. He reasoned that the falling water would transform its gravitational potential energy at the top into thermal energy at the bottom, where turbulence brings the water almost to a halt. If this transformation is the only process occurring, how much warmer will the water at the bottom be?
Answer:
Water becomes warmer by a temperature of ΔT = 0.119 K
Explanation:
If we assume that gravitational kinetic energy will be converyrf into thermal enrgy, we will have;
Q = U
So, m•c_w•ΔT = mgh
Where;
c_w is specific heat capacity of water with a value of 4184 J/Kg.K
ΔT is change in temperature indicating how warmer the water will be. Thus making ΔT the subject, we have;
ΔT = gh/c_w
So, ΔT = 9.8 x 51/4184 = 0.119 K
Answer:
2.8 cm
Explanation:
= Separation between two first order diffraction minima = 1.4 cm
D = Distance of screen = 1.2 m
m = Order
Fringe width is given by
Fringe width is also given by
For second order
Distance between two second order minima is given by
The distance between the two second order minima is 2.8 cm
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Answer:
0.6375 m/s
Explanation:
Let x be the distance of the man from the building
from the figure attached
initially the value of x=12
Given:
where the negative sign depicts that the distance of the man from the building is decreasing.
Now, Let The length of the shadow be = y
we have to calculate when x=4
from the similar triangles
we have,
or
Differentiating with respect to time 't' we get
or
Now for x = 4, and we have,
or
<u>here, the negative sign depicts the decrease in length and in the question it is asked the decreasing rate thus, the answer is </u><u>0.6375m/s</u>