A fireboat is to fight fires at coastal areas by drawing seawater with a density of 1030 kg/m3 through a 10-cm-diameter pipe at
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Answer:
(A) The tension's magnitude grows to four times the initial value, 4F.
Explanation:
When an object travels in a circular path, a centripetal force is exerted upon it. In this instance, the centripetal force acting on the stone can be represented by .
Here, m denotes the mass of the object
v is the velocity or speed of the object
r signifies the radius of the circular path
Importantly, the tension corresponds to the centripetal force.
Initially, the string completes one revolution each second, and subsequently, it accelerates to perform two revolutions in the same time frame. This signifies that the speed has increased twofold.
Applying our formula:F =
where F indicates the tension in the string
assuming the starting speed is v, after doubling it becomes 2v
Maintaining the circle's radius, we arrive at:
F=
From this equation, it's clear that the initial tension has quadrupled.
Consequently, the magnitude of the tension increases to four times its original value, 4F.
Answer:
The pen requires 7.2 mJ of energy to extend.
Explanation:
Provided:
Length = 1.8 cm
Spring constant = 300 N/m
Initial compression = 1.0 mm
Additional compression = 6.0 mm
Total compression = 1.0 + 6.0 = 7.0 mm
We need to determine the energy needed
This energy is equivalent to the variation in spring potential energy
Substitute the values into the formula
Therefore, a total of 7.2 mJ is needed to extend the pen.