Answer:
2/R*sqrt (g*s*sin(θ)) = w
Explanation:
Assume:
- The cylinder with mass m
- The radius of cylinder R
- Distance traveled down the slope is s
- The angular speed at bottom of slope w
- The slope of the plane θ
- Frictionless surface.
Solution:
- Using energy principle at top and bottom of the slope. The exchange of gravitational potential energy at height h, and kinetic energy at the bottom of slope.
ΔPE = ΔKE
- The change in gravitational potential energy is given as m*g*h.
- The kinetic energy of the cylinder at the bottom is given as rotational motion: 0.5*I*w^2
- Where I is the moment of inertia of the cylinder I = 0.5*m*R^2
We have:
m*g*s*sin(θ) = 0.25*m*R^2*w^2
2/R*sqrt (g*s*sin(θ)) = w
- The angular velocity depends on plane geometry θ , distance travelled down slope s, Radius of the cylinder R , and gravitational acceleration g
Answer:
3000 J
Explanation:
Kinetic energy is:
KE = ½ mv²
If m = 15 kg and v = -20 m/s:
KE = ½ (15 kg) (-20 m/s)²
KE = 3000 J
Answer: NNOOOOOOOOOOOOOOOOOOONONONO
Explanation: simple harmonic motion, in physics, repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side. The time interval of each complete vibration is the same. The force responsible for the motion is always directed toward the equilibrium position and is directly proportional to the distance from it. That is, F = −kx, where F is the force, x is the displacement, and k is a constant. This relation is called Hooke’s law.
A specific example of a simple harmonic oscillator is the vibration of a mass attached to a vertical spring, the other end of which is fixed in a ceiling. At the maximum displacement −x, the spring is under its greatest tension, which forces the mass upward. At the maximum displacement +x, the spring reaches its greatest compression, which forces the mass back downward again. At either position of maximum displacement, the force is greatest and is directed toward the equilibrium position, the velocity (v) of the mass is zero, its acceleration is at a maximum, and the mass changes direction. At the equilibrium position, the velocity is at its maximum and the acceleration (a) has fallen to zero. Simple harmonic motion is characterized by this changing acceleration that always is directed toward the equilibrium position and is proportional to the displacement from the equilibrium position. Furthermore, the interval of time for each complete vibration is constant and does not depend on the size of the maximum displacement. In some form, therefore, simple harmonic motion is at the heart of timekeeping.
Hello! Assuming that the only force acting on the mass is 30N...
Fnet = 30N
Fnet = ma (mass x acceleration)
ma = 30N
a = 30N / m
a = 30N / 7kg
a = 4.2857 m/s^2
a = 4 m/s^2
I hope this helps!
If the soloist produces "x" decibels and the 10-person choir produces "y" decibels, combined they will produce "x+y" decibels.
The second choir has 90 additional singers, we base our description on the first choir. If a 10-person choir produces "x+y" decibels, then the 90 person choir produces 10 (x+y) decibels.
