The density of polystyrene cube if 90% floats above the surface of water.
Expert Solution
Answer to Problem 3TP
The density of polystyrene cube if 90% floats above the surface is
Explanation of Solution
Given:
Density of water,
Volume of liquid,
Formula Used:
A polystyrene cube floating partially immersed in a container is considered. The relation between the density and volume of liquid and of object is given as,
Calculation:
Substitutefor V and for
Conclusion:
Therefore, the density of polystyrene cube if 90% floats above the surface is
To determine
(b)
The percentage of volume that remains outside of water.
Expert Solution
Answer to Problem 3TP
The percentage of volume remaining outside of water is 40%.
Explanation of Solution
Given:
Given:
Density of water,
Volume of liquid,
Mass,
Formula:
If the mass is located on polystyrene block, the total weight acting downwards will increases which causes the block to immerse still more.
Hence the equation becomes,
Where mass which placed over the block.
For solving, the equation can be rearranged,
Calculation:
Substitute for for 0.5 kg for mfor
Thus, the percentage of volume remaining outside of water is 40%.
Conclusion:
Therefore, the percentage of volume remains outside of water is 40%.
To determine
(c)
Whether or not, the block can remain partially submerged in the new fluid.
Whether or not, the block can remain partially submerged in ethyl alcohol with 0.5 kg mass placed on top.
Expert Solution
Answer to Problem 3TP
Yes, the block can remain partially submerged in ethyl alcohol.
Yes, the block can remain 76% submerged in ethyl alcohol with mass placed on top.
Explanation of Solution
Given:
Density,
Volume of liquid, Volume of liquid,
Mass,
Formula Used:
The volume of block immersed in alcohol with a mass is placed over the block is given as,
Calculation:
The object floats when its density is lesser than that of the fluid density. The density of ethyl alcohol isThe density of polystyrene block isTherefore, the block can remain partially submerged in ethyl alcohol.
Substitutefor for for m for
The volume fraction could be
Conclusion:
Therefore, the block can remain partially submerged in ethyl alcohol. The block can remain 76% submerged in ethyl alcohol with mass placed on top.
To determine
(d)
The way the density of polystyrene can be determined.
Expert Solution
Explanation of Solution
When the material is a spherical, the following steps can be used to find out the density.
The mass of the material should be found.
Use the thread to wrap the sphere for finding the circumference of the sphere.
The radius can be calculated from the circumference
The volume is calculated from the radius
The density of the material is found by using mass and radius by using the following equation
Conclusion:
Therefore,the density of polystyrene is determined without the water container by using spherical material by finding the radius and circumference of the sphere and the mass of the material.
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A block of mass m₁ = 10.0 kg is connected to a block of mass m₂ = 34.0 kg by a massless string that passes over a light, frictionless pulley. The 34.0-kg block is connected to a spring that has negligible mass and a force constant of k = 200 N/m as shown in the figure below. The spring is
unstretched when the system is as shown in the figure, and the incline is frictionless. The 10.0-kg block is pulled a distance h = 22.0 cm down the incline of angle 0 = 40.0° and released from rest. Find the speed of each block when the spring is again unstretched.
m/s
Vm1
Vm2
m/s
mi
m2
k
i
Truck suspensions often have "helper springs" that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as in the figure below. The helper spring engages when the main leaf spring is compressed by distance yo, and then helps to
support any additional load. Consider a leaf spring constant of 5.45 × 105 N/m, helper spring constant of 3.60 × 105 N/m, and y = 0.500 m.
Truck body
Dyo
Axle
(a) What is the compression of the leaf spring for a load of 4.90 × 105 N?
m
(b) How much work is done compressing the springs?
]
A skier of mass 75 kg is pulled up a slope by a motor-driven cable.
(a) How much work is required to pull him 50 m up a 30° slope (assumed frictionless) at a constant speed of 2.8 m/s?
KJ
(b) What power (expressed in hp) must a motor have to perform this task?
hp
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