A cylinder has a frictionless piston of mass m1=0.50 kg and radius 2.5 cm fitted
ID: 2276595 • Letter: A
Question
A cylinder has a frictionless piston of mass m1=0.50 kg and radius 2.5 cm fitted inside it. This mass is then attached via a light rope that passes over two massless, frictionless pulleys to another block m2=9.5 kg, as shown in the figure. The piston is open at the top and has a pump creating a reduced but constant pressure below m1. If the bock falls from rest a distance of 1.25m in 3.30s, what is the pressure beneath the piston?
A cylinder has a frictionless piston of mass m1=0.50 kg and radius 2.5 cm fitted inside it. This mass is then attached via a light rope that passes over two massless, frictionless pulleys to another block m2=9.5 kg, as shown in the figure. The piston is open at the top and has a pump creating a reduced but constant pressure below m1. If the bock falls from rest a distance of 1.25m in 3.30s, what is the pressure beneath the piston?Explanation / Answer
Let T = tension in the rope
For the second block,
m2g - T = m2 a, where a = acceleration of the block
For the piston,
T - (m1g - p*?r^2) = m1 a, where p = pressure difference across the piston.
Eliminating T from the two eqns.,
m2g - (m1g + p*?r^2) = (m1 + m2) a ... ( 1 )
For the motion of the second block,
1.25 = (1/2) a * (3.3)^2
=> a = 2.5 / (3.3)^2 = 0.23 m/s^2
Plugging this value of a and values of m1 and m2 and r in eqn. ( 1 ),
(9.5 - 0.5) * 9.8 - p * ? (0.025)^2 = (9.5 + 0.5) * (0.23)
=> 83 - 0.00196p = 2.15
=> p = (83 - 2.15) / (0.00196) = 43826.5 N/m^2
=> absolute pressure beneath the piston
=
? 5.7 x 10^4 N/m^2.
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