How is it that even light precipitation can still cause the collection of large amounts of water.
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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
Take the derivative to find the velocity of the object:
The object stops when :
so the answer is E.
Answer:
The change in momentum is
Explanation:
From the question we are told that
The time taken for the stone to stop is
The net force on the rock is
The impulse of the rock can be mathematically represented as
Substituting values
Now impulse is defined as the rate at which momentum change
Hence the change in momentum of the rock is equal to the impulse of the rock
So