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:
<em>The statement is true</em>
Explanation:
<u>Energy Conversion
</u>
When an object starts to fall in free air, it speeds up as it falls. The force of gravity acting on the object causes energy to be transferred from its gravitational potential energy to its kinetic energy. We can safely say the height converts to speed and vice-versa. If no external forces act on the system, we can easily calculate heights and speeds by knowing the total mechanical energy (gravitational potential plus kinetic) is conserved.
Answer:
Jupiter, Saturn, Uranus and Neptune collectively make up the group known as the jovian planets. The general structures of the jovian planets are opposite those of the terrestrial planets. Rather than having thin atmospheres around relatively large rocky bodies, the jovian planets have relatively small, dense cores surrounded by massive layers of gas. Made almost entirely of hydrogen and helium, these planets do not have solid surfaces.
The roller coaster is moving in a circular path, so the force that must be computed is the centripetal force. The centripetal force is the force acting on an object undergoing circular motion and is directed towards the center of the circular path. This is computed using:
F = mv²/r
F = (500 * 18²) / 12
F = 13,500 N
Now, at the bottom of the track, the track is also supporting the weight of the car and its passengers, which is:
W = mg
W = 500 * 9.81
W = 4,905 N
The total reactive force exerted by the track to counter the centripetal force and the weight of the car is:
F = 13,500 + 4,905
F = 18,405 Newtons
