A mass weighing 32 pounds stretches a spring 2 feet.
(a) Determine the amplitude and period of motion if the mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of 6 ft/s.
(b) How many complete cycles will the mass have completed at the end of 4 seconds?
Answer:
Period = 
seconds
8 cycles
Explanation:
A mass weighing 32 pounds stretches a spring 2 feet;
it implies that the mass (m) = 
m= 
= 1 slug
Also from Hooke's Law
2 k = 32
k = 
k = 16 lb/ft
Using the function:
(because of the initial position being above the equilibrium position)
( as a result of upward velocity)
NOW, we have:
However;
means
also implies that:
Hence, 
Period can be calculated as follows:
= 
= seconds
How many complete cycles will the mass have completed at the end of 4 seconds?
At the end of 4 seconds, we have:
cycles
(A) We can solve the problem by using Ohm's law, which states:
where
V is the potential difference across the electrical device
I is the current through the device
R is its resistance
For the heater coil in the problem, we know
and
, therefore we can rearrange Ohm's law to find the current through the device:
(B) The resistance of a conductive wire depends on three factors. In fact, it is given by:
where
is the resistivity of the material of the wire
L is the length of the wire
A is the cross-sectional area of the wire
Basically, we see that the longer the wire, the larger its resistance; and the larger the section of the wire, the smaller its resistance.
Answer:
b. Both stars will have the same shift.
Explanation:
It's a very simple problem to solve. Star 1 is approaching toward Earth with a speed v, so let's assume that the change in Doppler Shift is +F and Star 2 is moving away so the change in Doppler shift is -F. But it's time to notice the speed of both stars and that is same but only directions are different. speed is the main factor here. The magnitude of both shifts is F as we can see and + and - are showing there direction of motion. So, because of same amount of speed, both stars will have same shift magnitude. (Just the directions are different)
Balanced forces do not cause a change in motion. When balanced forces act on an object at rest, the object will not move. If you push against a wall, the wall pushes back with an equal
