Answer:
A) 138.8g
B)73.97 cm/s
Explanation:
K = 15.5 Kn/m
A = 7 cm
N = 37 oscillations
tn = 20 seconds
A) In harmonic motion, we know that;
ω² = k/m and m = k/ω²
Also, angular frequency (ω) = 2π/T
Now, T is the time it takes to complete one oscillation.
So from the question, we can calculate T as;
T = 22/37.
Thus ;
ω = 2π/(22/37) = 10.5672
So,mass of ball (m) = k/ω² = 15.5/10.5672² = 0.1388kg or 138.8g
B) In simple harmonic motion, velocity is given as;
v(t) = vmax Sin (ωt + Φ)
It is from the derivative of;
v(t) = -Aω Sin (ωt + Φ)
So comparing the two equations of v(t), we can see that ;
vmax = Aω
Vmax = 7 x 10.5672 = 73.97 cm/s
Answer:
a) 0 < r < R: E = 0, R < r < 2R: E = KQ/r^2, r > 2R: E = 2KQ/r^2
b) See the picture
Explanation:
We can use Gauss's law to find the electric field in all the regions:
EA = qen/e0 where qen is the enclosed charge
Remember that the electric field everywhere outside a sphere is:
E(r) = q/(4*pi*eo*r^2) = Kq/r^2
a)
- For 0 < r < R: There is not enclosed charge because all of it remains on the outer layer of the conducting sphere, therefore E = 0 EA = 0/e0 = 0 E = 0
- For R < r < 2R: Here the enclosed charge is equal Q E = Q/(4*pi*eo*r^2) = KQ/r^2
- For r > 2R: Here the enclosed charge is equal 2Q E = Q/(4*pi*eo*r^2) + Q/(4*pi*eo*r^2) = 2Q/(4*pi*eo*r^2) = 2KQ/r^2
b) At the beginning there is no electric field this is why you see a line in zero, In R the electric field is maximum and then it starts to decrease exponentially with the distance and finally in 2R the field increase a little due to the second sphere to then continue decreasing exponentially with the distance
Answer:
The equipment to use is: a beaker, a fixed amount of water, a thermometer.
The mass of water, the time, the temperature for each time should be noted and a graph of Temperature versus time should be made
Explanation:
The design of an experiment is to place the beaker in the microwave, with a good amount of water (approximately ⅔ of its capacity) and turn it on for small periods of time, generally the minimum is 30 s, quickly open the microwave, place a thermometer or better yet an infrared thermometer to measure the temperature of the water; repeat this several times.
The advantage of the infrared thermometer is that it reduces the transfer of heat between the water and the thermometer.
The mass of water, the time, the temperature for each time should be noted and a graph of Temperature versus time should be made.
The equipment to use is: a beaker, a fixed amount of water, a thermometer.
The main precaution that must be taken is not to open the microwave while it is on.
Explanation:
By Hooke's Law, Fe = kx.
Since Fe = 1.6N and x = 9.2cm - 8cm = 1.2cm,
k = Fe/x = 1.6N/1.2cm = 1.33N/cm.
