Two cylinders with the same mass density C = 713 kg / m 3 are floating in a cont
ID: 1494993 • Letter: T
Question
Two cylinders with the same mass density C = 713 kg / m3 are floating in a container of water (with mass density W= 1025 kg / m3). Cylinder #1 has a length of L1 = 20 cm and radius r1 = 5 cm. Cylinder #2 has a length of L2 = 10 cmand radius r2 = 10 cm. If h1 and h2 are the heights that these cylinders stick out above the water, what is the ratio of the height of Cylinder #2 above the water to the height of Cylinder #1 above the water (h2 / h1)?
h2 / h1 =
A helium balloon ride lifts up passengers in a basket. Assume the density of air is 1.28 kg/m3 and the density of helium in the balloon is 0.18 kg/m3. The radius of the balloon (when filled) is R = 4.7 m. The total mass of the empty balloon and basket is mb = 128 kg and the total volume is Vb = 0.061 m3. Assume the average person that gets into the balloon has a mass mp = 74 kg and volume Vp = 0.077 m3.
1)
What is the volume of helium in the balloon when fully inflated?
m3
2)
What is the magnitude of the force of gravity on the entire system (but with no people)? Include the mass of the balloon, basket, and helium.
N
3)
What is the magnitude of the buoyant force on the entire system (but with no people)? Include the volume of the balloon, basket, and helium.
N
4)
What is the magnitude of the force of gravity on each person?
N
5)
What is the magnitude of the buoyant force on each person?
N
6)
How many FULL people can the balloon lift up? (Your answer must be an integer.)
people
A water pipe tapers down from an initial radius of R1 = 0.21 m to a final radius of R2 = 0.11 m. The water flows at a velocity v1 = 0.83 m/s in the larger section of pipe.
1)
What is the volume flow rate of the water?
m3/s
2)
What is the velocity of the water in the smaller section?
m/s
3)
Using this water supply, how long would it take to fill up a swimming pool with a volume of V = 165 m3? (give your answer in minutes)
min
4)
The water pressure in the center of the larger section of the pipe is P1 = 253250 Pa. Assume the density of water is 103 kg/m3.
What is the pressure in the center of the smaller section of the pipe?
Pa
5)
If the pipe was turned vertical and the volume flow rate in the larger section is kept the same, which answers would change?
the speed of water in the smaller section
the volume flow rate in the smaller section
the pressure in the smaller section
A storm blows wind across the top of a roof at a speed of v = 26.3 m/s. Assume the air on the lower side of the roof (inside) is at rest and the roof is flat and has an area A = 39 m2. The density of air is 1.28 kg/m3.
1)
What is the pressure differential across the top and bottom of the roof?
Pa
2)
What is the net lift force on the roof due to the storm?
N
A block with mass m =6.5 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.24 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.2 m/s. The block oscillates on the spring without friction.
1)
What is the spring constant of the spring?
N/m
2)
What is the oscillation frequency?
Hz
3)
After t = 0.41 s what is the speed of the block?
m/s
4)
What is the magnitude of the maximum acceleration of the block?
m/s2
5)
At t = 0.41 s what is the magnitude of the net force on the block?
N
6)
Where is the potential energy of the system the greatest?
At the highest point of the oscillation.
At the new equilibrium position of the oscillation.
At the lowest point of the oscillation.
A block with mass m = 5.1 kg is attached to two springs with spring constants kleft = 31 N/m and kright = 56 N/m. The block is pulled a distance x = 0.24 m to the left of its equilibrium position and released from rest.
1)
What is the magnitude of the net force on the block (the moment it is released)?
N
2)
What is the effective spring constant of the two springs?
N/m
3)
What is the period of oscillation of the block?
s
4)
How long does it take the block to return to equilibrium for the first time?
s
5)
What is the speed of the block as it passes through the equilibrium position?
m/s
6)
What is the magnitude of the acceleration of the block as it passes through equilibrium?
m/s2
7)
Where is the block located, relative to equilibrium, at a time 1.02 s after it is released? (if the block is left of equilibrium give the answer as a negative value; if the block is right of equilibrium give the answer as a positive value)
m
8)
What is the net force on the block at this time 1.02 s? (a negative force is to the left; a positive force is to the right)
N
9)
What is the total energy stored in the system?
J
10)
If the block had been given an initial push, how would the period of oscillation change?
the period would increase
the period would decrease
the period would not change
At t = 0 a block with mass M = 5 kg moves with a velocity v = 2 m/s at position xo = -.33 m from the equilibrium position of the spring. The block is attached to a massless spring of spring constant k = 61.2 N/m and slides on a frictionless surface. At what time will the block next pass x = 0, the place where the spring is unstretched?
t1 =
seconds
At t = 0 a block with mass M = 5 kg moves with a velocity v = 2 m/s at position xo = -.33 m from the equilibrium position of the spring. The block is attached to a massless spring of spring constant k = 61.2 N/m and slides on a frictionless surface. At what time will the block next pass x = 0, the place where the spring is unstretched?
t1 =
seconds
A simple pendulum with mass m = 1.5 kg and length L = 2.44 m hangs from the ceiling. It is pulled back to an small angle of = 9.3° from the vertical and released at t = 0.
1)
What is the period of oscillation?
s
2)
What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0?
N
3)
What is the maximum speed of the pendulum?
m/s
4)
What is the angular displacement at t = 3.63 s? (give the answer as a negative angle if the angle is to the left of the vertical)
°
5)
What is the magnitude of the tangential acceleration as the pendulum passes through the equilibrium position?
m/s2
6)
What is the magnitude of the radial acceleration as the pendulum passes through the equilibrium position?
m/s2
7)
Which of the following would change the frequency of oscillation of this simple pendulum?
increasing the mass
decreasing the initial angular displacement
increasing the length
hanging the pendulum in an elevator accelerating downward
PLEASE, CLEARLY WORK IT OUT EACH QUESTIONS CORRECTLY..THNK YOU SO MUCH!!!
Explanation / Answer
For Cylinder 1:
Vsub/Vtotal = c/w
=> r12h1/(r12L1) = c/w
=> h1 = (c/w)L1
Similarly, h2 = (c/w)L2
So, h2/h1 = L2/L1 = 10/20 = 0.5
(NOTE: You are only supposed to ask one question at a time)
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