Answer:
a) 
b) 
Explanation:
Let's find the radius of the circumference first. We know that bob follows a circular path of circumference 0.94 m, it means that the perimeter is 0.94 m.
The perimeter of a circunference is:
Now, we need to find the angle of the pendulum from vertical.
Let's apply Newton's second law to find the tension.
We use centripetal acceleration here, because we have a circular motion.
The vertical equation of motion will be:
(1)
The horizontal equation of motion will be:
(2)
a) We can find T usinf the equation (1):
We can find the angular velocity (ω) from the equation (2):
b) We know that the period is T=2π/ω, therefore:
I hope it helps you!
Answer:
a = 0.009 J
b = 0.19 m/s
c = 0.005 J and 0.004 J
Explanation:
Given that
Mass of the object, m = 0.5 kg
Spring constant of the spring, k = 20 N/m
Amplitude of the motion, A = 3 cm = 0.03 m
Displacement of the system, x = 2 cm = 0.02 m
a
Total energy of the system, E =
E = 1/2 * k * A²
E = 1/2 * 20 * 0.03²
E = 10 * 0.0009
E = 0.009 J
b
E = 1/2 * k * A² = 1/2 * m * v(max)²
1/2 * m * v(max)² = 0.009
1/2 * 0.5 * v(max)² = 0.009
v(max)² = 0.009 * 2/0.5
v(max)² = 0.018 / 0.5
v(max)² = 0.036
v(max) = √0.036
v(max) = 0.19 m/s
c
V = ±√[(k/m) * (A² - x²)]
V = ±√[(20/0.5) * (0.03² - 0.02²)]
V = ±√(40 * 0.0005)
V = ±√0.02
V = ±0.141 m/s
Kinetic Energy, K = 1/2 * m * v²
K = 1/2 * 0.5 * 0.141²
K = 1/4 * 0.02
K = 0.005 J
Potential Energy, P = 1/2 * k * x²
P = 1/2 * 20 * 0.02²
P = 10 * 0.0004
P = 0.004 J
A. Larger. It is larger Bc they r all larger than the other
It depends on "Potential Energy", the amount energy it could have, the amount depending on certain circumstances, like height or force. This was how traditional and some modern rollercoasters work. As the "conveyer belt" pulls you up, the higher you go, the more potential energy you have. Once you are falling down the hill, you are experiencing "Kinetic Energy". Hope it makes sence.
