Answer:
Explanation:
The instantaneous velocity of a point mass that executes a simple harmonic movement is given by:
Where:
Express the amplitude in meters:
The angular frequency can be found using the next equation:
Using the data provided:
At the equilibrium position:
Answer:
B
Explanation:
for the motion every night, it is because the Earth spins on its axis.
for the changes over a year, this is because the Earth rotates around the sun.
for the changes over hundreds, thousands or millions of years, this is because the whole solar system (including the Earth, of course) rotates with all the other stars in our galaxy around the center of the galaxy. and each star system has its own orbit (similar to the planets in our solar system).
it is very rare to see objects outside of our galaxy without a telescope, but they change too over a long period of time, because our galaxy not only rotates by also moves through the universe, and these other objects move on their own too.
The equation to be used is the derived formulas for rectilinear motion at a constant acceleration. The formula for acceleration is
a = (v - v₀)/t
where
v and v₀ are the initial and final velocities, respectively
t is the time
a is the acceleration
Since it started from rest, v₀ = 0. Using the formula:
0.15 m/s² = (v - 0)/[2 minutes*(60 s/1 min)]
Solving for v,
v = 18 m/s
Answer:
(a) 1.21 m/s
(b) 2303.33 J, 152.27 J
Explanation:
m1 = 95 kg, u1 = - 3.750 m/s, m2 = 113 kg, u2 = 5.38 m/s
(a) Let their velocity after striking is v.
By use of conservation of momentum
Momentum before collision = momentum after collision
m1 x u1 + m2 x u2 = (m1 + m2) x v
- 95 x 3.75 + 113 x 5.38 = (95 + 113) x v
v = ( - 356.25 + 607.94) / 208 = 1.21 m /s
(b) Kinetic energy before collision = 1/2 m1 x u1^2 + 1/2 m2 x u2^2
= 0.5 ( 95 x 3.750 x 3.750 + 113 x 5.38 x 5.38)
= 0.5 (1335.94 + 3270.7) = 2303.33 J
Kinetic energy after collision = 1/2 (m1 + m2) v^2
= 0.5 (95 + 113) x 1.21 x 1.21 = 152.27 J
Answer:
270 m/s²
Explanation:
Given:
α = 150 rad/s²
ω = 12.0 rad/s
r = 1.30 m
Find:
a
The acceleration will have two components: a radial component and a tangential component.
The tangential component is:
at = αr
at = (150 rad/s²)(1.30 m)
at = 195 m/s²
The radial component is:
ar = v² / r
ar = ω² r
ar = (12.0 rad/s)² (1.30 m)
ar = 187.2 m/s²
So the magnitude of the total acceleration is:
a² = at² + ar²
a² = (195 m/s²)² + (187.2 m/s²)²
a = 270 m/s²
