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Answer:
The answer is below
Explanation:
A diver works in the sea on a day when the atmospheric pressure is 101 kPa. The diver uses compressed air to breathe under water. 1700 litres of air from the atmosphere is compressed into a 12-litre gas cylinder. The compressed air quickly cools to its original temperature. Calculate the pressure of the air in the cylinder.
Solution:
Boyles law states that the volume of a given gas is inversely proportional to the pressure exerted by the gas, provided that the temperature is constant.
That is:
P ∝ 1/V; PV = constant
P₁V₁ = P₂V₂
Given that P₁ = initial pressure = 101 kPa, V₁ = initial volume = 1700 L, P₂ = cylinder pressure, V₂ = cylinder volume = 12 L. Hence:
P₁V₁ = P₂V₂
100 kPa * 1700 L = P₂ * 12 L
P₂ = (100 kPa * 1700 L) / 12 L
P₂ = 14308 kPa
Answer:
a) A=0.125 m
b) T = 1.72 s
c) f= 0.58 Hz
Explanation:
a) As we are told that the maximum displacement from the equilibrium position was 0.125 m (from which it was released at zero initial speed), this is the amplitude of the resultant SHM, so, A=0.125 m
b) In order to find the period, we must get the total time needed to complete a full cycle (which means that the block must pass twice through the equilibrium point). We are told that at t=0.860 sec, the block has reached to the other end of the trajectory, and it has passed through the equilibrium point only once.
This means that the period must be exactly the double of this time:
T = 2*0. 860 sec = 1.72 sec.
c) In a SHM, the frequency is defined just as the inverse of the period (like in a uniform circular movement), so we can get the frequency f as follows:
f = 1/T = 1/ 1.72 s= 0.58 Hz
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