An unruly student with a spitwad (a lump of wet paper) of mass 20 g in his pocket finds himself in the school library where there is a ceiling fan overhead. He relieves his boredom by throwing the spitwad up at the ceiling fan where it collides with, and sticks to, the end of one of the blades of the stationary ceiling fan. Its horizontal velocity vector is perpendicular to the long axis of the blade. If the fan is free to rotate (no friction at all) and has moment of inertia I=1.4kgm2 , if the spitwad has horizontal velocity 4 m/s, and if the spitwad sticks to the fan blade at a distance of 0.6 m from the rotation axis of the fan, how much time will it take the fan to move through one complete revolution after the spitwad hits it (closest answer)?a. 1min
b. 2min
c. 3min
d. 4min
e. 5min
f. 6min
Answers
Answer:
T = 188.5 s, correct is C
Explanation:
This problem must be worked on using conservation of angular momentum. We define the system as formed by the fan and the paper, as the system is isolated, the moment is conserved
initial instant. Before the crash
L₀ = r m v₀ + I₀ w₀
the angular speed of the fan is zero w₀ = 0
final instant. After the crash
L_f = I₀ w + m r v
L₀ = L_f
m r v₀ = I₀ w + m r v
angular and linear velocity are related
v = r w
w = v / r
m r v₀ = I₀ v / r + m r v
m r v₀ = (I₀ / r + mr) v
v =
let's calculate
v =
v =
v = 0.02 m / s
To calculate the time of a complete revolution we can use the kinematics relations of uniform motion
v = x / T
T = x / v
the distance of a circle with radius r = 0.6 m
x = 2π r
we substitute
T = 2π r / v
let's calculate
T = 2π 0.6/0.02
T = 188.5 s
reduce
t = 188.5 s ( 1 min/60 s) = 3.13 min
correct is C
Related Questions
A spherical shell rolls without sliding along the floor. The ratio of its rotational kinetic energy (about an axis through its center of mass) to its translational kinetic energy is:
The normal is a line perpendicular to the reflecting surface at the point of incidence.
A heavy object and a light object are dropped from the same height. If we neglect air resistance, which will hit the ground first?
How can socialism impact populations?
Answers
Answer
3.340J
Explanation;
Using the relation. Energy stored in capacitor = U = 7.72 J
U =(1/2)CV^2
C =(eo)A/d
C*d=(eo)A=constant
C2d2=C1d1
C2=C1d1/d2
The separation between the plates is 3.30mm . The separation is decreased to 1.45 mm.
Initial separation between the plates =d1= 3.30mm .
Final separation = d2 = 1.45 mm
(A) if the capacitor was disconnected from the potential source before the separation of the plates was changed, charge 'q' remains same
Energy=U =(1/2)q^2/C
U2C2 = U1C1
U2 =U1C1 /C2
U2 =U1d2/d1
Final energy = Uf = initial energy *d2/d1
Final energy = Uf =7.72*1.45/3.30
(A) Final energy = Uf = 3.340J
(b) the exergy destroyed during this process.
Answers
A) The exergy of the refrigerant at the initial and final states are :
- Initial state = - 135.5285 kJ
- Final state = -51.96 kJ
B) The exergy destroyed during this process is : - 1048.4397 kJ
Given data :
Mass ( M ) = 5 kg
P1 = 0.7 Mpa = P2
T1 = 60°C = 333 k
To = 24°C = 297 k
P2 = 100 kPa
A) Determine the exergy at initial and final states
At initial state :
U = 274.01 kJ/Kg , V = 0.034875 m³/kg , S = 1.0256 KJ/kg.k
exergy ( Ф ) at initial state = M ( U + P₂V - T₀S )
= 5 ( 274.01 + 100* 10³ * 0.034875 - 297 * 1.0256)
≈ - 135.5285 kJ
At final state :
U = 84.44 kJ / kg , V = 0.0008261 m³/kg, S = 0.31958 kJ/kg.k
exergy ( ( Ф ) at final state = M ( U + P₂V - T₀S )
= -51.96 kJ
B) Determine the exergy destroyed
exergy destroyed = To * M ( S2 - S1 )
= 297 * 5 ( 0.31958 - 1.0256 )
= - 1048.4397 KJ
Hence we can conclude that A) The exergy of the refrigerant at the initial and final states are : Initial state = - 135.5285 kJ, Final state = -51.96 kJ and The exergy destroyed during this process is : - 1048.4397 kJ
Learn more about exergy : brainly.com/question/25534266
Final answer:
Exergy of refrigerant-134a at initial and final states is obtained from property tables and by multiplying the mass of the refrigerant with its specific exergy at each state. The difference in exergy between the two states represents the exergy destroyed.
Explanation:
To solve the given question, we need the property values of
refrigerant-134a
at the initial and the final states.
At an initial state of 0.7 MPa and 60°C, the specific exergy for refrigerant-134a can be obtained from property tables which are standard in thermodynamics textbooks. Same for the final state at 0.7 MPa and 24°C, the specific exergy can be obtained from the same property tables.
The exergy of the refrigerant at the initial and the final states can be calculated by multiplying the mass of the refrigerant with its specific exergy at each state.
Exergy destruction during this process can be calculated using the relation between exergy change and exergy destruction. The exergy change of a system between initial and final states is equal to the difference of the exergy of the system at final and initial states.
Based on the second law of thermodynamics, the difference in exergy should be equal to the exergy destroyed during the process.
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Answers
Answer:
d' = 75.1 cm
Explanation:
It is given that,
The actual depth of a shallow pool is, d = 1 m
We need to find the apparent depth of the water in the pool. Let it is equal to d'.
We know that the refractive index is also defined as the ratio of real depth to the apparent depth. Let the refractive index of water is 1.33. So,
or
d' = 75.1 cm
So, the apparent depth is 75.1 cm.
The apparent depth of a 1.00-meter-deep pool, when viewed from above, is around 75.2 centimeters. This difference is due to light refraction in water, causing optical distortion.
When observing a shallow pool of 1.00 meter depth from above, the apparent depth is altered by the phenomenon of light refraction in water. Light bends as it passes from air into water, affecting the way objects are perceived underwater.
The apparent depth is less than the actual depth due to this bending of light. To calculate the apparent depth, one can use the Snell's Law formula, which relates the angles of incidence and refraction to the refractive indices of the two media.
However, a simplified formula for the apparent depth (d') in terms of the actual depth (d) is given by d' = d/n, where 'n' is the refractive index of water (approximately 1.33). Therefore, in this case, the pool's apparent depth, when viewed from above, will be approximately 75.2 centimeters, making it shallower than it appears at first glance due to the optical effects caused by light traveling through water.
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Complete question below:
"What is the apparent depth, in centimeters, when looking straight down at a shallow pool that is 1.00 meter deep? Note that the apparent depth is different from the actual depth due to the refraction of light in water."
Answers
Answer:TL;DR: 3.535 cm
Explanation:
Xcm = ΣxMoments/ΣMasses = (10*0 + 10*5)/(10+10) = 50/20 = 2.5 cm
by symmetry,
Ycm = 2.5 cm
The distance D from the point Xcm,Ycm to the origin is D = √(2.5²+2.5²) = 3.535 cm
Final answer:
The center of mass of the bent wire is approximately 11.18 cm from the bend.
Explanation:
In order to find the center of mass of the bent wire, we need to divide it into two segments: the horizontal segment and the vertical segment. The length of each segment is half of the total length of the wire, which is 20 cm, so each segment is 10 cm long.
The center of mass of the horizontal segment is located exactly at its middle point, which is 5 cm from the corner. The center of mass of the vertical segment is also located at its middle point, which is 10 cm from the corner. Since the horizontal and vertical segments are orthogonal, the distance from the bend to the center of mass of the bent wire is the hypotenuse of a right triangle with legs of length 5 cm and 10 cm. Using the Pythagorean theorem, we can calculate the distance:
d = sqrt(5^2 + 10^2) = sqrt(25 + 100) = sqrt(125) = 11.18 cm
Therefore, the center of mass of the bent wire is approximately 11.18 cm from the bend.
Answers
Answer:
67.5 cm
Explanation:
u = - 90 cm, v = 3 x u = 3 x 90 = 270 cm
let f be the focal length
Use lens equation
1 / f = 1 / v - 1 / u
1 / f = 1 / 270 + 1 / 90
1 / f = 4 / 270
f = 67.5 cm
Final answer:
To determine the focal length of the lens, we use the lens formula and set up an equation based on the given information. Solving for the image distance, we find that it is zero, indicating the image is formed at infinity. Therefore, the focal length of the lens is 90 cm.
Explanation:
To determine the focal length of the lens, we can use the lens formula:
1/f = 1/v - 1/u
Where f is the focal length, v is the image distance, and u is the object distance.
Given that the image distance triples when the object is moved from infinity to 90 cm in front of the lens, we can set up the following equation:
1/f = 1/(3v) - 1/(90)
Multiplying through by 90*3v, we get:
90*3v/f = 270v - 90*3v
90*3v/f = 270v - 270v
90*3v/f = 0
Simplifying further, we find that: v = 0
When the image distance is zero, it means the image is formed at infinity, so the lens is focused at the focal point. Therefore, the focal length of the lens is 90 cm.
a pool to the north end of the pool, a distance of 28 meters. What is the
swimmer's velocity?
A. 1.3 m/s south
B. 1.3 m/s north
C. 0.8 m/s south
D. 0.8 m/s north
Answers
The correct answer is B. 1.3 m/s north
Explanation:
Velocity is a factor that describes how fast or slow the motion of a body occurs and its direction. Moreover, this can be calculated by dividing the total displacement into the time of movement, and the final result is expressed in units such as meters per second followed by the direction, for example, 152 m/s south. The process to calculate the velocity of the swimmer is shown below.
This means the velocity of the swimmer is 1.27 m/s, which can be rounded as 1.3 m/s. Additionally, if the direction is considered it would be 1.3 m/s north because the swimmer went from the south of the pool to its north.
Answer:
the answer is B
Explanation:
confirmed