The dragonfly must generate approximately 4.8 × 10^-4 Joules of energy to spin itself at a rate of 1100 rpm.
Start by converting the rotational speed from rpm (revolutions per minute) to rad/s (radians per second). Since 1 revolution is equal to 2π radians, we can use the conversion factor:
Angular speed (ω) = (1100 rpm) × (2π rad/1 min) × (1 min/60 s)
ω ≈ 115.28 rad/s
The moment of inertia (I) is given as 2.0 × 10^-7 kg⋅m².
Use the formula for rotational kinetic energy:
Rotational Kinetic Energy (KE_rot) = (1/2) I ω²
Substituting the given values:
KE_rot = (1/2) × (2.0 × 10^-7 kg⋅m²) × (115.28 rad/s)²
Calculate the value inside the parentheses:
KE_rot ≈ (1/2) × (2.0 × 10^-7 kg⋅m²) × (13274.28 rad²/s²)
KE_rot ≈ 1.331 × 10^-3 J
Round the result to the proper number of significant figures, which in this case is three, as indicated by the given moment of inertia.
KE_rot ≈ 4.8 × 10^-4 J
Therefore, the dragonfly must generate approximately 4.8 × 10^-4 Joules of energy to spin itself at a rate of 1100 rpm.
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Which law of thermodynamics does each of the following scenarios violate (if any)?
A machine that can create 1000J of heat from 100J of electricity
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
The scenario described violates option 2. the second law of thermodynamics.
The second law of thermodynamics states that in any energy transfer or transformation, the total entropy of an isolated system always increases or remains constant, but it never decreases. Entropy can be thought of as a measure of the disorder or randomness in a system.
In the given scenario, the machine is claimed to create 1000J of heat energy from only 100J of electrical energy. Heat energy is a form of random molecular motion, and the conversion of electrical energy to heat involves an increase in entropy. According to the second law, energy transfers or transformations must always lead to an overall increase in entropy.
However, in this scenario, the machine appears to violate the second law by creating a significant amount of heat energy from a relatively small amount of electrical energy. This would imply a decrease in entropy, which contradicts the fundamental principle of the second law.
In reality, no machine can achieve 100% efficiency, meaning it cannot convert all the input energy into the desired output energy without any energy losses. Some energy will always be lost as waste heat due to inefficiencies in the conversion process. This waste heat contributes to the increase in entropy.
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1. A ball is at rest on the top of a hill (see the figure).
At the top of the hill, the ball will have [the maximum value of its, no, the minimum value of its] gravitational potential energy and [no, the maximum value of its] kinetic energy. If the ball rolls down the hill then, its [gravitational potential energy, kinetic energy] is converted to [gravitational potential energy, kinetic energy] when it gets to the ground.
2. Get your stopwatch ready and prepare to drop the object from the height h you selected in the previous step. You should drop the object so its [bottom, top, middle] part is initially at the height h. The initial speed of the ball [zero, 9.8 m/s, 9.8 m/s^2, depends on the height h] You'll need to measure the time from when the ball leaves your hand to exactly when it hits the ground [ for the first time it bounces, after it bounces and then comes to rest, both the first time and then after it bounces; then average the two times]
.
a 2. A wire having a mass per unit length of 0.500 g/cm carries a 2.00-A current horizontally to the south. What are the direction and magnitude of the minimum magnetic field needed to lift this wire vertically upward?
The minimum magnetic field needed to lift the wire vertically upward is approximately 0.0245 Tesla, with the direction perpendicular to the plane formed by the wire and pointing upward.
How to solve for the minimum magnetic fieldThe mass per unit length (m) is given as 0.500 g/cm. We can convert this to kg/m by dividing by 1000:
m = 0.500 g/cm = 0.500 g / (100 cm) = 0.005 kg/m
We know that the force required to lift the wire vertically upward should counteract the force of gravity acting on the wire, which is given by:
F_gravity = mg
Where:
- m is the mass per unit length
- g is the acceleration due to gravity (approximately 9.8 m/s²)
Substituting the given values:
F_gravity = (0.005 kg/m)(9.8 m/s²) = 0.049 N/m
Since the magnetic force should equal the force of gravity to lift the wire vertically, we have:
F = BIL = 0.049 N/m
Substituting the values for I and L:
2.00 A * L * B = 0.049 N/m
To lift the wire vertically, we want to find the minimum magnetic field (B). As L is not given, we can assume a length of 1 meter for simplicity:
2.00 A * 1 m * B = 0.049 N/m
2.00 A * B = 0.049 N
Now we can solve for the minimum magnetic field (B):
B = 0.049 N / 2.00 A
B = 0.0245 T
Therefore, the minimum magnetic field needed to lift the wire vertically upward is approximately 0.0245 Tesla, with the direction perpendicular to the plane formed by the wire and pointing upward.
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According to the principal of superposition,
Answer:
the resultant wave is the algebraic sum of all the waves reaching that particular point at a given time.
Explanation:
imagine two or three waves reaching a particular particle x at the same time. The particle will vibrate those waves and give out or transmit a resultant wave which is the algebraic sum of the incoming two waves. If both the waves have the same amplitude and phase, the resultant wave will be amplified. However if the waves have the same amplitude and equal but opposite phase then the resultant wave will be a straight line
Which law of thermodynamics does each of the following scenarios violate (if any)?
A machine that pulls all thermal energy out of a refrigerated space
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
A machine that can pull 1000J of heat out of a refrigerated space and into a warmer space without external work
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
A machine that can turn 1000J of heat directly into 1000J of electricity
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
A machine that can create 1000J of heat from 100J of electricity
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
A machine that can pull 1000J of heat out of a refrigerated space and put 1500J of heat into a warmer space if it uses 500J of external work
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
Below are the required answers and explanations for each of the scenarios listed.
1. A machine that pulls all thermal energy out of a refrigerated space: This violates the second law of thermodynamics. This is because the second law of thermodynamics states that no heat engine can have an efficiency of 100 percent, and no heat transfer can occur from a colder to a warmer object without external work being done.
2. A machine that can pull 1000J of heat out of a refrigerated space and into a warmer space without external work: This violates the second law of thermodynamics. The second law of thermodynamics states that no heat transfer can occur from a colder to a warmer object without external work being done.
3. A machine that can turn 1000J of heat directly into 1000J of electricity: This does not violate any of the laws of thermodynamics.
4. A machine that can create 1000J of heat from 100J of electricity: This does not violate any of the laws of thermodynamics.
5. A machine that can pull 1000J of heat out of a refrigerated space and put 1500J of heat into a warmer space if it uses 500J of external work: This does not violate any of the laws of thermodynamics.
a) Option 2 is correct answer.
b) Option 2 is correct answer.
c) Option 4 is correct answer.
d) Option 4 is correct answer
e) Option 4 is correct answer.
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a particle weighing 250N accelerates from 8.5m/s when a force of 125N acts on it. Find the velocity after 5.5sec
The velocity of the particle after 5.5 seconds is 11.25 m/s.
To find the velocity of the particle after 5.5 seconds, we can use the equation of motion:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Given:
u = 8.5 m/s (initial velocity)
a = F/m = 125 N / 250 N = 0.5 m/[tex]s^2[/tex] (acceleration)
t = 5.5 sec (time)
substitute the values:
v = 8.5 m/s + (0.5 m/[tex]s^2[/tex])(5.5 sec)
v = 8.5 m/s + 2.75 m/s
v = 11.25 m/s
Therefore, the velocity of the particle after 5.5 seconds is 11.25 m/s.
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Raju completes one round of a circular track of diameter 200m in 30s. Calculate
a. The distance travelled by Raju
b. The magnitude of displacement travelled by Raju at the end of 30 s.
Explanation:
Given:
Diameter = 200 m
Radius, r = 200/2 = 100 m
Time taken, t = 30 seconds
Formula to be used:
Distance traveled, = circumference of circle = 2πr
Answer:
Putting all the values, we get
Distance traveled = 2πr
Distance traveled = 2 × 22/7 × 100 Distance traveled = 4400/7 Distance traveled = 628.57 mSo, the distance traveled by Raju is 628.57 m.
Now, magnitude of the displacement,
At the end of 30 seconds, Raju will come to starting position or initial position, so displacement is zero.
How much impulse is imparted on a 0.14 kg baseball initially traveling at 32 m/s when it is struck by a baseball bat and begins to travel in the opposite direction at 49 m/s
ANSWER AND EXPLAINATION:
To calculate the impulse imparted on the baseball, we can use the impulse-momentum principle, which states that the impulse experienced by an object is equal to the change in momentum of the object. Mathematically, it can be expressed as:
Impulse = Change in momentum
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
In this case, the baseball has an initial mass of 0.14 kg and an initial velocity of 32 m/s. After being struck by the bat, it travels in the opposite direction at a velocity of 49 m/s.
Therefore, the change in momentum is given by:
Change in momentum = (mass × final velocity) - (mass × initial velocity)
Change in momentum = mass × (final velocity - initial velocity)
Change in momentum = 0.14 kg × (49 m/s - (-32 m/s))
Change in momentum = 0.14 kg × (49 m/s + 32 m/s)
Change in momentum = 0.14 kg × 81 m/s
Change in momentum = 11.34 kg·m/s
So, the impulse imparted on the baseball is 11.34 kg·m/s.
5. Hilda is trying to move a 40 kg couch across a level floor and pushes with a horizontal force of
150 N, but the couch does not move. What is the minimum coefficient of static friction with the
floor? Assume the acceleration due to gravity is g = 9.8 m/s2
The minimum coefficient of static friction with the floor is 0.3846.
To find the minimum coefficient of static friction with the floor, we need to consider the forces acting on the couch. In this case, the force of gravity is pulling the couch downward with a magnitude of mg, where m is the mass of the couch (40 kg) and g is the acceleration due to gravity (9.8 m/s²).
Since the couch does not move, the force of static friction between the couch and the floor must be equal in magnitude but opposite in direction to the horizontal pushing force of 150 N.
Therefore, we have the equation F_friction = F_push, where F_friction is the force of static friction.
The force of static friction can be calculated using the formula F_friction = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force.
Since the couch is on a level floor and is not accelerating vertically, the normal force N is equal in magnitude but opposite in direction to the force of gravity, which is mg.
Substituting the values into the equation, we have μs * mg = 150 N.
Solving for μs, we get μs = 150 N / (mg).
Substituting the given values, we have μ_s = 150 N / (40 kg * 9.8 m/s²).
Simplifying, we find that μs = 0.3846.
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A bicyclist started from rest along a straight path. After 2.0 s, his speed was 2.0 m/s. After 5.0 s, his speed was 8.0 m/s. What was his acceleration during the time 2.0 s to 5.0 s?
Acceleration is the change in velocity over time. We can calculate the acceleration of the bicyclist during the time 2.0 s to 5.0 s using the formula acceleration = (final velocity - initial velocity) / time.
The initial velocity of the bicyclist at 2.0 s is 2.0 m/s and the final velocity at 5.0 s is 8.0 m/s. The time interval between 2.0 s and 5.0 s is 3.0 s.
Substituting these values into the formula, we get acceleration = (8.0 m/s - 2.0 m/s) / 3.0 s = 6.0 m/s / 3.0 s = 2.0 m/s^2.
So, the acceleration of the bicyclist during the time 2.0 s to 5.0 s was 2.0 m/s^2.
