How much work is done by a force F → = (2 x N) i ^ + (3 N) j ^ , with x in meters, that moves a particle from a position r → i =(2 m) i ^ + (3 m) j ^ to a position r → f = -(4 m) i ^ − (3 m) j ^ ?
How much work is done by a force F → = (2 x N) i ^ + (3 N) j ^ , with x in meters, that moves a particle from a position r → i =(2 m) i ^ + (3 m) j ^ to a position r → f = -(4 m) i ^ − (3 m) j ^ ?
How much work is done by a force
F
→
= (2x N)
i
^
+ (3 N)
j
^
, with x in meters, that moves a particle from a position
r
→
i
=(2 m)
i
^
+ (3 m)
j
^
to a position
r
→
f
= -(4 m)
i
^
− (3 m)
j
^
?
You are using a microscope to view a dust particle suspended in a drop of water on a microscope slide. As water molecules bombard the particle, it "jitters" about in a random motion (Brownian motion). The particle's average kinetic energy is the same as
3
that of a molecule in an ideal gas (K =
The particle (assumed to be spherical) has a density of 350 kg/m³ in water at 23°C.
2
BT).
(a) If the particle has a diameter d, determine an expression for its rms speed in terms of the diameter d. (Enter your answer as a multiple of d−3/2. Assume v
is in m/s and d-3/2 is in m−3/2. Do not include units in your answer.)
rms
V.
=
rms
rms
Obtain an expression for v by equating the expression for the kinetic energy of the particle in terms of v
obtain an expression for the mass of the particle in terms of its diameter. d-3/2
rms
to the expression for the average kinetic energy of a molecule. Knowing the density of the particle and assuming it is a sphere, we can
(b) Assuming the particle moves at a…
You are watching a new bridge being built near your house. You notice during the construction that two concrete spans of the bridge of total length L; = 270 m are placed end to end so that no room is allowed for expansion (figure (a)). In the opening
storyline for the thermodynamics chapter, we talked about buckling sidewalks. The same thing will happen with spans on bridges if allowance is not made for expansion (figure (b)). You want to warn the construction crew about this dangerous situation, so
you calculate the height y to which the spans will rise when they buckle in response to a temperature increase of AT = 19.0°C.
a
b
T
T+AT
y =
Ider Enter a number. made by one span, with its thermally expanded length as the hypotenuse.
An open cylinder of air has a radius of 38.0 cm and a height of 50.0 cm, as shown in figure (a).
50.0 cm
Ah
The air pressure is 1.00 atm and the temperature is 13.5°C. A 25.0 kg piston is then lowered onto the cylinder, forming an airtight seal, as shown in figure (b). The air inside is compressed until the piston reaches equilibrium (mechanical and thermal), and
at this point the piston is a height h; from the bottom of the cylinder. Lastly, a 27.5 kg dog steps onto the piston, and the air in the cylinder again compresses, as show in figure (c). After reaching equilibrium, the air inside is again at 13.5°C, and the
height of the piston decreases a distance Ah as shown.
(a) What is the distance Ah (in mm) that the piston moves when the dog is on it?
mm
(b) To what temperature (in °C) should the gas be warmed to raise the piston and the dog back to h;?
°C
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