What would be the height of the atmosphere if the air density (a) were uniform and (b) decreased linearly to zero with height? Assume that at sea level the air pressure is 1.0 atm and the air density is 1.3 kg/
The height of the atmosphere would be 7951.33 m.
We are given that,
Pressure = P = 1 atm
Air density = ρ = 1.3 kg/m³
Therefore, the height of the atmosphere when the density is constant can be calculated by,
P = ρ g h
We know that pressure at sea level = 1 atm = 101300 Pa
Thus , putting the values in the above equation,
h = (101300 Pa)/(1.3 kg/m³)(9.8m/s²)
h = 7951.33 m
Therefore, the height of the atmosphere would be 7951.33 m, when the air density is constant.
Note : the correct order of the question is,
Assume that at sea-level the air pressure is 1.0 atm and the air density is 1.3 kg/m3.(a) What would be the height of the atmosphere if the air density were constant?(b) What would be the height of the atmosphere if the air density decreased linearly to zero with height?
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Problem 12.41 9 of 9 Review A 50 g mass rotates in a vertical plane--call it the xy-plane with the y-axis pointing up--at the end of a 75-cm-long, massless, rigid rod. The other end of the rod is attached to a frictionless pivot at the origin. Part A What is the gravitational torque about the pivot when the mass is 60° above the +x-axis? Give your answer using unit vectors. Express your answer in newton-meters. Enter components of torque, separated by comma. IVO AE ? Tx, Ty,Tz = N·m Submit Request Answer
The value of gravitational torque after solving the expression will be equal to -0.18375 N.mz.
What is Torque?The rotating equivalent of a force in physics or mechanics is called torque. Depending on the topic matter, it may also be referred to as the moment, point in time of force, rotating force, or turning effect. It symbolizes a force's capacity to cause a change inside the bodies natural rotational motion.
As per the given information in the question,
Mass, m = 50 g
Length, l = 75 cm
Gravitational force, [tex]\vec F[/tex] = -mgy
Then, the position vector of the particle will be,
[tex]\vec \tau[/tex] = l(cos 60° x + sin 60° y) × (-mgz)
= -0.18375 N.mz
Therefore,
[tex]\tau_x, \tau_y,\tau_z=0, 0, -0.18375[/tex]
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a block is pulled along a surface of negligible friction by a spring scale that exerts a force f on the block. the mass of the block is 4kg, and the spring scale reads 10n. which of the following free-body diagrams can be used to show the magnitude and direction of all the forces exerted on the block as it is pulled along the surface?
The correct free-body diagram is the one shown in option C
What is the correct free-body diagram?We know that the free-body diagram could be used to identify the forces that are acting on an object. We know that the normal force that acts on an object must be equal to the weight of the object and this is represented as lines of equal length on the free-body diagram.
We can now see that the correct free-body diagram is one in which the magnitude of the force weight and the normal force is the same. Now the force on the spring would be shown as the forward force.
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