The 'spot' at the end of the laser beam moves in a circle. The radius of the circle is the distance between the laser and the spot.
The circumference of every circle is (2π) · (radius) .
The speed of the spot is (distance) / (time) .
Speed = (circumference) / (time to turn once around the full circle)
<u><em>Speed = </em></u>
<u><em>(circumference) · (nr of revs) / (second) .</em></u>
(a). Speed = (2π) (8km) · (9 rev) / sec
Speed = (2π · 8 · 9) km/sec
Speed = 144π km/sec
<em>Speed = 452.4 km/sec</em>
(b). Speed = (2π) (16km) · (9 rev) / sec
Speed = (2π · 16 · 9) km/sec
Speed = 288π km/sec
<em>Speed = 904.8 km/sec</em>
(c). 300,000 km/sec = (2π · distance) · (9 / sec)
300,000 km = (18π · distance)
Distance = 300,000 / 18π km
<em>Distance = 5,305 km</em>
Electrons are negatively charged particles whereas protons are positively charged particles.
When a negative is shown on the bar, this means that the difference between the electrons and protons is a negative value, which also means that the number of electrons (negative particles) is more than the number of protons (positive particles).
Based on the above, the correct choice would be:
<span>D. There are more electrons than protons
</span>
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Answer:
k = 1073.09 N/m
A = 0.05 m
Explanation:
Given:
- Time period T = 0.147 s
- maximum speed V_max = 2 m/s
- mass of the block m = 0.67 kg
Find:
- The spring constant k
- The amplitude of the motion A.
Solution:
- A general simple harmonic motion is modeled by:
x (t) = A*sin(w*t)
- The velocity of the above modeled SHM is:
v = dx / dt
v(t) = A*w*cos(w*t)
- Where A is the amplitude in meters, w is the angular speed rad/s and time t is in seconds.
- We can see that maximum velocity occurs when (cos(w*t)) maximizes i.e it is equal to 1 or -1. Hence,
- V_max = A*w
- Where w is related to mass of the object and spring constant k as follows,
w = sqrt ( k / m )
- The relationship between w angular speed and Time period T is:
w = 2*pi / T
- Equating the above two equations we have,
m*(2*pi / T)^2 = k
- Hence, k = 0.67*(2*pi / 0.157)^2
k = 1073.09 N / m
- So, amplitude A is:
A = V_max*sqrt ( m / k )
A = 2*sqrt ( 0.67 / 1073.09 )
A = 0.05 m