Because solar panels are man made so they can shut down, not move, break, etc...? Don’t judge me, it’s just a guess.
1) At the moment of being at the top, the piston will not only tend to push the penny up but will also descend at a faster rate at which the penny can reach in 'free fall', in that short distance. Therefore, at the highest point, the penny will lose contact with the piston. Therefore the correct answer is C.
2) To solve this problem we will apply the equations related to the simple harmonic movement, hence we have that the acceleration can be defined as
Where,
a = Acceleration
A = Amplitude
= Angular velocity
From a reference system in which the downward acceleration is negative due to the force of gravity we will have to
From the definition of frequency and angular velocity we have to
Therefore the maximum frequency for which the penny just barely remains in place for the full cycle is 2.5Hz
Electric cars, Remove CO2, Burning fossil fuel
Do you remember the general equation for the distance covered
by a moving object ? There are not many perfect opportunities to
use it in all its glory, but I think this is one of them.
Position =
(starting distance) + (starting speed) (time) + (1/2) (acceleration) (time)²
H = starting position + (starting speed x t) + 1/2 A t²
Here's how we can use it, with some careful definitions:
-- Let's say the surface of the sea is zero height.
Then 'H' ... the position at the end ... is zero, when it plunks into the water, and
the starting, original position of the stone is +10 on the cliff in the man's hand.
-- Starting speed is +5 ... 5 m/s upward, when he tosses it.
-- Acceleration is 9.8 m/s² downward ... the acceleration of gravity.
I think this is going to work out just beautifully !
0 = (5) + 5t - 1/2 (9.8) t²
-4.9 t² + 5t + 5 = 0 That's the whole thing right there. Look how gorgeous that is !
Solve it for 't' with the quadratic equation,
A = -4.9
B = 5
C = 5
When you solve a quadratic with the formula, you always get two roots.
If it's a real-world situation, one of them might not make sense. That's
the result in this case.
The two roots are
t = - 0.622 second
and
t = + 1.642 second
The first one isn't useful, because it means 0.622 second <u>before</u> the man
tossed the stone up.
So our answer is: We hear the 'plunk' <em>1.642 second</em> after the upward toss.
Answer:
T=0.372 s, f=2.7 Hz, w=16.9 rad/s, k=179.2 N/m, v= 8.78 m/s, F= 48.4 N
Explanation:
a.)
Period: It is already given in the question "oscillator repeats its motion every 0.372 s".
So T=0.372 s
b)
frequency= f = 1/ T
f = 1/ 0.372
f=2.7 Hz
c).
Angular frequency= w= 2πf
w= 2*π*2.7
w=16.9 rad/s
d)
Spring Constant:
As w=
⇒w²= k/m
⇒k= m*w²
⇒k= 0.628 * 16.9² N/m
⇒k=179.2 N/m
e)
The mass will have maximum speed when it passes through the mean position.
At mean position
Maximum elastic potential energy = Maximum kinetic energy
1/2 k A² = 1/2 m v² ( A is amplitude of oscillation)
⇒ v=
⇒ v= \
⇒ v= 8.78 m/s
f)
Maximum force will be exerted on the block when it is at maximum distance.
F= k* A ( A is amplitude of oscillation)
F= 179.2 * 0.27 N
F= 48.4 N