The block's speed at the point where x=0.25A is v = 31.95 cm/s.
<h3>What is Spring constant?</h3>
The spring stiffness is quantified by the spring constant, or k. For various springs and materials, it varies. The stiffer the spring is and the harder it is to stretch, the bigger the spring constant.
question is incomplete, this is the remaining statement
What is the amplitude of the subsequent oscillations? And What is the block's speed at the point where x=0.25A?
x = Asin(wt)
v = Aw coswt
at t = 0
w = sqrt(k/m)
v = Aw
A = v/w
A = 7.17 cm
part b )
E = 1/2mv^2 + 1/2kx^2 = 1/2kA^2
mv^2 + k(1/4A)^2 = 1/2kA^2
mv^2 + kA^2/16 = kA^2
mv^2 = kA^2 - kA^2/16
mv^2 = 15kA^2/16
v^2 = 15/16 * (k/m) * A^2
v^2 = 15/16 *w^2A^2
v = sqrt(15/16) * wA
v = 31.95 cm/s
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Answer:
<em>The object could fall from six times the original height and still be safe</em>
Explanation:
<u>Free Falling</u>
When an object is released from rest in free air (no friction), the motion is completely dependant on the acceleration of gravity g.
If we drop an object of mass m near the Earth surface from a height h, it has initial mechanical energy of
When the object strikes the ground, all the mechanical energy (only potential energy) becomes into kinetic energy
Where v is the speed just before hitting the ground
If we know the speed v is safe for the integrity of the object, then we can know the height it was dropped from
Solving for h
If the drop had occurred in the Moon, then
Where hM, vM and gM are the corresponding parameters on the Moon. We know v is the safe hitting speed and the gravitational acceleration on the Moon is g_M=1/6 g
This means the object could fall from six times the original height and still be safe
Answer: 4.8 s
Explanation:
We have the following data:
the mass of the raft
the force applied by Sawyer
the raft's final speed
the raft's initial speed (assuming it starts from rest)
We have to find the time 
Well, according to Newton's second law of motion we have:
(1)
Where 
is the acceleration, which can be expressed as:
(2)
Substituting (2) in (1):
(3)
Where 
Isolating from (3):
(4)
Finally:
Try the solutions described in the attached picture, note the answers are marked with green colour.
<span> In radioactive decay, an unstable atomic nucleus emits particles or radiation and converts to a different atomic nucleus. If the new nucleus is unstable, it will decay again, until eventually, a stable nucleus is formed. Such a sequence of nuclear decays forms a decay series.
The half-life of a radioactive substance is the time required for half of the atoms of a radioactive isotope to decay. If you have, say, 1 million atoms of a specific isotope in a sample, the time required for 500,000 of those atoms to decay is the half-life of that specific isotope. If you have 50 atoms of that isotope, 25 atoms will decay in the same amount of time.
Because the half-life is fixed for a specific isotope, it can be used to date objects. You compare the decay rate of an old object with the decay rate of a fresh sample. Nuclear decay is a first-order process and can be described by a specific mathematical equation, which depends on the decay rate and the half-life. Knowing those values, you can work back and determine the age of an object, as compared with a standard sample. Old objects will not have as much of a radioactive isotope in them as new objects, since the isotopes will have decayed over time in the old object.</span>
