NEED ANSWER ASAP
2 answers:
You might be interested in
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
Answer:
The tension in the string is quadrupled i.e. increased by a factor of 4.
Explanation:
The tension in the string is the centripetal force. This force is given by
m is the mass, v is the velocity and r is the radius.
It follows that , provided m and r are constant.
When v is doubled, the new force, , is
Hence, the tension in the string is quadrupled.