Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.97 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.)
A)If a helium nucleus scatters to an angle of 116° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. b) What is the final kinetic energy (in J) of the helium nucleus?
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A heat engine made with an ideal gas with f = 5 degrees of freedom has 3 steps. Starting with a volume of 8 liters and a pressure of 1.3 × 10^5 Pa, the gas is compressed adiabatically to a volume of 1 liter and a pressure P2. Next the gas expands at constant pressure back to 8 liters, then the pressure drops at constant volume back to 1.3×10^5 Pa. Draw the cycle in a P −V diagram. Calculate the pressure P2. Calculate the efficiency of the engine. Calculate the ratio Tmin/Tmax of minimum and maximum temperatures during the cycle and compare the efficiency of this engine to eCarnot of a Carnot engine operating with the same value of Tmin/Tmax.
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if a rocket was orbiting a planet and then the mass of the planet suddenly decreased what would happen to the movement of the rocket?
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A computer disk drive is turned on starting from rest and has constant angular acceleration.
Part A
If it took 0.420 s for the drive to make its second complete revolution, how long did it take to make the first complete revolution?
Part B
What is its angular acceleration, in rad/s2?
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Explain the differences between primary electrons, secondary electrons, Auger electrons, and backscattered electrons and how they are used in SEM imaging and analysis
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47. a) Imagine that you are conducting an activity
with a laser to create an interference
pattern. Use the appropriate equations to predict two
ways (other than the way
described in the following example) to change the
interference pattern in order to
have closer fringes. Explain your predictions.
Here’s an example to get you started:
According to the equation
Δx = Lλ/d ,
the distance between the fringes (∆x) is proportional
to the wavelength (since
they are both numerators). This means that increasing
one will increase the other.
Therefore, decreasing the wavelength will decrease the
distance between the fringes.
(Hint: You can use the “Thomas Young’s Double-slit
Experiment” simulation from
this lesson to verify your
predictions.)
b) If you were using a hands-on activity to verify
your predictions and use
measurements to determine the wavelength of the laser
being used, describe any
safety precautions you would take and sources of error
that you might encounter. Be
sure to explain how you might reduce the effects of
the sources of error.
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1) projectile blitz:
a) given an initial velocity (Vx0,Vy0) off a cliff of height H,
what
is the final velocity? What is the horizontal distance
traveled? How much time is the projectile in the air for?
b) given a launch angle theta for the same case of
launching off a
cliff of height H, and given a horizontal distance d to a target
that
the projectile is supposed to hit, what speed should the projectile
be
launched at?
2) Liz May is travelling South with speed Vm.
Jagmeet Singh is travelling
west with speed Vs. At time 0, May is a distance Ym North of
a
political intersection, and Singh is Xs to the east of the
intersection. Find the distance of closest approach.
3) A person of mass m is on a massless weight scale in
an elevator of
mass M being pulled up by a cable with tension T. The tension is
large
enough to cause positive vertical acceleration. What weight does
the
scale read?
4) What banking angle for a circular race track of
radius R would
be optimal for race cars going speed V?
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1) A cylinder of Mass M and radius R, and initial
speed V, starts
rolling up an incline of angle theta relative to horizontal.
Assuming
no slipping, how high up does the cylinder get?
2) teeter/totter
a) Peewee has mass m and his big buddy Delilah has mass 2m. If
Peewee
sits at one end of a uniform teeter totter of length L and mass M,
how
far from the central pivot should Delilah sit (ie on the other end)
to
be balanced?
b) Delilah instead chooses to sit at the far end from
Peewee. What
vertical acceleration does Peewee experience when they start from
a
level teeter/totter from 0 angular velocity at horizontal? Provide
an
answer that is a function of the angular displacement (theta) from
the
horizontal. What normal force does Peewee experience as a function
of
theta?
3) A baseball-crazy astronaut in space catches a
fastball. What happens?
Let's treat the astronaut as a rod of length L and mass M and
assume
the ball of mass m attaches a distance L/5 from one
end. Compute/describe the resultant motion. Note the moment of
inertia
for a solid rod is ML^2/12 for rotation around its center of mass.
Hint,
you will have to use the parallel axis theorem for moment of
inertia.
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An open container holds ice of mass 0.570 kg at a temperature of -13.7 ∘C. The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 730 J/minute. The specific heat of ice to is 2100 J/kg⋅K and the heat of fusion for ice is 334×10^3 J/kg.
A) How much time [tmelts] passes before the ice starts
to melt?
B)From the time when the heating begins, how much time [trise]does
it take before the temperature begins to rise above 0∘C?
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A cell phone sends and receives electromagnetic waves in the microwave frequency range.
a) Explain the physics of how an oscillator creates these waves.
b) Research the possible side effects of using cell phones. Citing at least three websites
that you consider reliable, write a short 100- to 150-word paragraph summarizing
three main conclusions based on your research and your opinion; in other words, will
your cell phone usage change, based on what you have learned?
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#5b. Suppose that the two masses in the previous problem remains separated by a distance d meters, but the second mass is replaced by a mass that is 8.0 times smaller than the one it replaces. In terms of F, the original force on each of the masses, what is the magnitude of the force on the first mass now? Give your answer in the form "(a.bcd)F" N.
#5a. The magnitude of the gravitational force that a point mass exerts on another point mass when they are separated by a distance of d meters if F Newton. Now suppose that the second mass is moved so that the distance between them is now 0.68d meters. What is the magnitude of the new force that this second mass will experience at this new location? Give your answer in terms of F. For example, if the force is 7.85 times F then your answer would be (7.85)F. If the force is 0.55 times F then your answer would be (0.55)F. Give your answer rounded to 2 decimal places.
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Explain why the classical theory of light as an electromagnetic wave (or of electrons as particles) is unable to explain the following phenomena whereas quantum mechanics is successful.
(1) The turn-on voltage of differently colored LEDs
(2) The existence of transparent conductors
(3) The decrease in frequency of photons scattered off of atoms
(4) The spectrum of blackbody emission
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