13.)Two objects are connected by a light string passing over a light, frictionle
ID: 1784844 • Letter: 1
Question
13.)Two objects are connected by a light string passing over a light, frictionless pulley as shown in the figure below. The object of mass m1 = 6.40 kg is released from rest at a height h = 5.20 m above the table.
(a) Using the isolated system model, determine the speed of the object of mass m2 = 3.00 kg just as the 6.40–kg object hits the table.
What is the relationship between the speed of block m1 and the speed of block m2? When block m1 reaches the table, what is the height of block m2? m/s
(b) Find the maximum height above the table to which the 3.00–kg object rises.
Do you need to use energy conservation for this part of the problem? m
16.)Sewage at a certain pumping station is raised vertically by 5.87 m at the rate of 1 880 000 liters each day. The sewage, of density 1 050 kg/m3, enters and leaves the pump at atmospheric pressure and through pipes of equal diameter.
(a) Find the output mechanical power of the lift station.
W
(b) Assume an electric motor continuously operating with average power 4.05 kW runs the pump. Find its efficiency.
%
Explanation / Answer
Que. (16)
Given Data
h = 5.87 m,
V = 1880000 liters
= 1880 m^3 [since 1 liter = 10^-3 m^3]
rho = 1050 kg/m^3
t = 1 day
= 86400 s
Input power, Pin = 4.05 kW
= 4050 W
(a)
Output power, Pout = W / t
= m g h / t
= rho*V*g*h / t
= 1050 * 1880 * 9.8 * 5.87 / 86400
= 1314.30 W
Output power, Pout = 1314.30 W
(b)
efficiency = (Pout / Pin) * 100
= (1314.30 / 4050 ) * 100
= 32.45
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