Answer: Potassium iodide
Explanation: their you go
Answer:
Potassium iodide
Explanation:
Have a good day
What happens to the temperature of a substance while it is changing state?
Answer:
its temperature stays constant
Explanation:
Which of the following is true of a boat moving on water with
no net force acting on it?*
A. It is rising with increasing speed.
B. It is sinking with increasing speed.
C. It is traveling at a constant velocity.
D. It is accelerating forward.
A tennis ball is shot vertically upward inside a tower with an initial speed of
20.0 m/s. Neglect air resistance. Approximately how long does it take the tennis ball to reach its maximum height?
0.50 s
2.04 s
4.08 s
6.08 s
9.80 s
Determine the velocity of the ball 3.0 s after it is thrown
9.40 m/s, downward
9.40 m/s, upward
29.4 m/s, downward
38.8 m/s, upward
38.8 m/s, downward
The ball's height at time t is
y = (20.0 m/s) t - 1/2 g t²
where g is the acceleration due to gravity, with magnitude 9.80 m/s².
Also, recall that
v² - u² = 2 a ∆y
where u is the initial velocity, v is the final velocity, a is the acceleration, and ∆y is the change in height. Let Y be the maximum height. At this height, v = 0, so
- (20.0 m/s)² = 2 (-g) Y
==> Y ≈ 20.408 m
Plug this into the first equation and solve for t :
Y = (20.0 m/s) t - 1/2 (9.80 m/s²) t²
==> t ≈ 2.04 s
The ball's velocity at time t is
v = 20.0 m/s - g t
After t = 3.0 s, its velocity will be
v = 20.0 m/s - (9.80 m/s²) (3.0 s)
v = -9.40 m/s
or 9.40 m/s in the downward direction.
The modern model of the atom describes electrons in a little less specific detail than earlier models did. Why is it that being less sure about the placement of electrons in an atom is actually an improvement over earlier models?
The plum pudding model of the atom states that
Answer:
It is because one cannot know exactly the position of the electron within the atom.
One formulation of Heisenberg's Uncertainty Principle tells us that one cannot know simultaneously the position and momentum of the electron, so one cannot specify exactly either coordinate because the other would be infinite.
Bohr specified the most probable position of the electron at its lowest energy level in hydrogen and the product of the two would be about the Heisenberg value.
I
2800000 kg
Fig. 2.1
The total mass of the rocket and its full load of fuel is 2.8 106 kg. The constant force provided by
the rocket's motors is 3.2 x 107N.
32000000 N.
(a) Calculate
(i) the total weight of the rocket and the fuel.
weight =
Answer:
W = 27468000 [N] or 27.47 [kN]
Explanation:
The weight of a body is defined as the product of mass by gravitational acceleration.
\(W = m*g\)
where:
W = weight of the rocket with fuel [kg]
m = mass = 2800000 [kg]
g = gravity acceleration = 9.81 [m/s²]
Now we can solve:
\(W = 2800000*9.81\\W = 27468000 [N]\)
g Design an experiment you can use to determine the mass of the metal cylinder. When you explain your experiment, be sure to mention: What is the underlying model (equation) that you can use to determine the mass from your measurements
Answer:
m = \(\frac{k}{g}\) x,
graph of x vs m
Explanation:
For this exercise, the simplest way to determine the mass of the cylinder is to take a spring and hang the mass, measure how much the spring has stretched and calculate the mass, using the translational equilibrium equation
F_e -W = 0
k x = m g
m = \(\frac{k}{g}\) x
We are assuming that you know the constant k of the spring, if it is not known you must carry out a previous step, calibrate the spring, for this a series of known masses are taken and hung by measuring the elongation (x) from the equilibrium position, with these data a graph of x vs m is made to serve as a spring calibration.
In the latter case, the elongation measured with the cylinder is found on the graph and the corresponding ordinate is the mass
A 0.009 kg bullet fired through a door enters at 803 m/s and leaves at 617 m/s. If the door material is known to exert an average resistive force of 5620 N on bullets of this type at usual speeds, find the thickness of the door.
Answer:
The thickness of the door is 0.4230 m
Explanation:
Given;
mass of bullet, m = 0.009 kg
initial velocity of the bullet, u = 803 m/s
final velocity of the bullet, v = 617 m/s
average resistive force of the door on the bullet, F = 5620 N
Apply Newton's second law of motion;
Force exerted by the door on the bullet = Force of the moving bullet
F = ma
where;
F is applied force
m is mass
a is acceleration
Also, Force exerted by the door on the bullet = Force of the moving bullet
\(F =ma, \ But \ a =\frac{dv}{dt} = \frac{u-v}{t} \\\\F = \frac{m(u-v)}{t}\)
where;
v is the final velocity of the bullet
u is initial velocity of the bullet
t is time
We need to calculate the time spent by the bullet before it passes through the door.
\(t = \frac{m(u-v)}{F} \\\\t = \frac{0.009(803-617)}{5620} = 0.0002979 \ s\)
Distance traveled by the bullet within this time period = thickness of the door
This distance is equivalent to the product of average velocity and time
\(S = (\frac{u+v}{2}) t\)
where;
s is the distance traveled
\(S = (\frac{u+v}{2}) t\\\\S = (\frac{803+617}{2}) 0.0002979\\\\S = 0.4230 \ m\)
Therefore, the thickness of the door is 0.4230 m
1. The kinetic energy of a car is 8 106 J as it travels along a horizontal road. How much work is required to stop the car in 10 s? (A) zero joules (B) 8 105 J (C) 8 107 J (D)8 104 J (E) 8 106 J
The power to stop the car with kinetic energy of a car is \(8*10^{6} J\) as it travels along a horizontal road is \(8*10^{5} watt\), option B
What is Kinetic energy ?Kinetic energy can be seen as one that is been recorded when an object is able to move from a place , in a broad term we can say this is the energy that can be attributed to that of someone leaving a place and go to another place hence we can see it as the one in the motion.
The definition of energy as the "power to accomplish work" refers to the capacity to apply a force that moves an object. Even if the word is vague, it is clear what energy actually means: it is the force that causes objects to move. The two types can be attributed to the one we know which are kinetic and potential energy.
\(Power \frac{Energy}{time}\)
\(Energy = 8*10^{6} J\)
\(time = 10 s\)
\(Power = \frac{8*10^{6} J}{10}\)
\(power = 8*10^{5} watt\)
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proper question;
The kinetic energy of a car is 8 × 106 J as it travels along a horizontal road. How much power is required to stop the car in 10 s? (A) zero joules (B) 8 105 J (C) 8 107 J (D)8 104 J (E) 8 106 J
find the power of a lift that transfers 450 J of energy in 15 seconds.
Answer: P=30W
Explanation:
formula is p=w/t
p = power
w = work
t = elapsed time
input variables, solve then simplify.
The power of a lift that transfers 450 J of energy in 15 seconds is 30 watts.
Power is defined as the rate of doing work, i.e. the amount of work done per unit time.
Mathematically, it can be represented as follows:
Power = Work done / time taken
Therefore, the power of a lift that transfers 450 J of energy in 15 seconds can be calculated as follows:
Power = Work done / time taken= 450 J / 15 s= 30 W
Therefore, the power of the lift is 30 watts.
To explain further, we know that power is measured in watts (W), and it is the rate at which work is done or energy is transferred.
Here, we are given that the lift transfers 450 J of energy in 15 seconds.
We can find the power of the lift by dividing the amount of work done by the time taken to do it. By substituting the given values, we get the power of the lift as 30 W.
In simple terms, this means that the lift can transfer energy at a rate of 30 joules per second. This can also be interpreted as the lift can do 30 joules of work in one second.
Hence, we can conclude that the power of the lift is 30 watts.
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Objectives
Pecina
y
01:Posttest 01:Motion Along a Straight Line
eration
1. An elevator moving down passes its neighbor, an elevator moving up. Their speed relative to one another is 8 m/s. What is the velocity of each
elevator relative to someone standing on the first floor? Assume that the elevators are traveling at the same speed, and that the upward direction is
positive.
tant Acceleration
O Both elevators are moving at 8 m/s.
y Falling Objects
O One elevator is moving at 4 m/s; the other elevator is moving at -4 m/s.
O Both elevators are moving at 4 m/s.
tive Velocity
O One elevator is moving at 8 m/s; the other elevator is moving at -8 m/s.
Posttest
on in a Plane
ton's Laws of Motion
>
1 of 25
Submit
blications of Newton's
Description
440
11:53 PM
4/4/2021
Answer:
B
Explanation: Given that an elevator moving down passes its neighbor, an elevator moving up. Their speed relative to one another is 8 m/s. What is the velocity of each elevator relative to someone standing on the first floor? Assume that the elevators are traveling at the same speed, and that the upward direction is positive.
O Both elevators are moving at 8 m/s.
y Falling Objects
O One elevator is moving at 4 m/s; the other elevator is moving at -4 m/s.
O Both elevators are moving at 4 m/s.
tive Velocity
O One elevator is moving at 8 m/s; the other elevator is moving at -8 m/s.
Solution.
Since the upward direction is positive, the downward direction will be negative.
For their speed relative to one another to be 8 m/s, the individual velocity will be:
4 - ( - 4 ) = 8
Therefore, the correct answer is:
One elevator is moving at 4 m/s; the other elevator is moving at -4 m/s
Which is option B
Because the negative sign multiply by negative sign will give positive.
That is,
4 + 4 = 8
At a fabrication plant, a hot metal forging has a mass of 90.8 kg, and a specific heat capacity of 434 J/(kg C°). To harden it, the forging is quenched by immersion in 689 kg of oil that has a temperature of 38.3°C and a specific heat capacity of 2680 J/(kg C°). The final temperature of the oil and forging at thermal equilibrium is 58.9°C. Assuming that heat flows only between the forging and the oil, determine the initial temperature in degrees Celsius of the forging.
The initial temperature of the forging is approximately 1,090.42°C.
To determine the initial temperature of the forging, we can use the principle of conservation of energy. The heat lost by the forging is equal to the heat gained by the oil during the quenching process.
The heat lost by the forging can be calculated using the formula:
Q_lost = m_forging * c_forging * (T_forging_initial - T_equilibrium)
where:
- Q_lost is the heat lost by the forging
- m_forging is the mass of the forging (90.8 kg)
- c_forging is the specific heat capacity of the forging (434 J/(kg C°))
- T_forging_initial is the initial temperature of the forging (unknown)
- T_equilibrium is the final temperature of the oil and forging at thermal equilibrium (58.9°C)
The heat gained by the oil can be calculated using the formula:
Q_gained = m_oil * c_oil * (T_equilibrium - T_oil_initial)
where:
- Q_gained is the heat gained by the oil
- m_oil is the mass of the oil (689 kg)
- c_oil is the specific heat capacity of the oil (2680 J/(kg C°))
- T_oil_initial is the initial temperature of the oil (38.3°C)
Since the heat lost by the forging is equal to the heat gained by the oil, we can set up the following equation:
m_forging * c_forging * (T_forging_initial - T_equilibrium) = m_oil * c_oil * (T_equilibrium - T_oil_initial)
Plugging in the given values, we can solve for T_forging_initial:
90.8 kg * 434 J/(kg C°) * (T_forging_initial - 58.9°C) = 689 kg * 2680 J/(kg C°) * (58.9°C - 38.3°C)
Simplifying the equation:
90.8 * 434 * (T_forging_initial - 58.9) = 689 * 2680 * (58.9 - 38.3)
Solving for T_forging_initial:
T_forging_initial - 58.9 = (689 * 2680 * (58.9 - 38.3)) / (90.8 * 434)
T_forging_initial = 58.9 + (689 * 2680 * (58.9 - 38.3)) / (90.8 * 434)
Calculating the value:
T_forging_initial ≈ 1,090.42°C
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6.
least 2 m. If the same car is moving with the speed 80K/h,what is the minimum stopping distance?
A car moving with a speed of 40 km/h can be stopped by applying the brakes after at-
The minimum stopping distance of the car is determined as 8 m.
What is the minimum stopping distance?The minimum stopping distance of the car is calculated as follows;
d = (u²)/(2a)
where;
d is the minimum stopping distanceu is the initial velocitya is the acceleration of the carwhen the minimum stopping distance = 2 m, initial velocity = 40 km/hr = 11.11 m/s
2 = (11.11²)/(2a)
a = (11.11²)/(2 x 2)
a = 30.86 m/s²
when the speed becomes 80 km/h, the minimum stopping distance is calculated as;
u = 80 km/h = 22.22 m/s
d = (22.22² )/ (2 x 30.86)
d = 8 m
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Two identical loudspeakers 2.00 m apart are emitting sound waves into a room where the speed of sound is 340 m/s. Abby is standing 5.00 m in front of one of the speakers, perpendicular to the line joining the speakers, and hears a maximum in the intensity of the sound.
Required:
What is the lowest possible frequency of sound for which this is possible?
Answer:
The lowest possible frequency of sound for which this is possible is 1307.69 Hz
Explanation:
From the question, Abby is standing 5.00m in front of one of the speakers, perpendicular to the line joining the speakers.
First, we will determine his distance from the second speaker using the Pythagorean theorem
l₂ = √(2.00²+5.00²)
l₂ = √4+25
l₂ = √29
l₂ = 5.39 m
Hence, the path difference is
ΔL = l₂ - l₁
ΔL = 5.39 m - 5.00 m
ΔL = 0.39 m
From the formula for destructive interference
ΔL = (n+1/2)λ
where n is any integer and λ is the wavelength
n = 1 in this case, the lowest possible frequency corresponds to the largest wavelength, which corresponds to the smallest value of n.
Then,
0.39 = (1+ 1/2)λ
0.39 = (3/2)λ
0.39 = 1.5λ
∴ λ = 0.39/1.5
λ = 0.26 m
From
v = fλ
f = v/λ
f = 340 / 0.26
f = 1307.69 Hz
Hence, the lowest possible frequency of sound for which this is possible is 1307.69 Hz.
In a plane, add a 120 N force at 300 and a -100 N force at 900 using the parallelogram method. [111N 339]
See the attached figure.
The black arrows represent the two given vectors. The dashed black arrows are these same vectors, but translated so that the end of one vector is aligned with the start of another.
The red vector is their sum.
In case you also need to find the magnitude and direction of the sum, we have
A = (120 N) (cos(30°) i + sin(30°) j) = (60√3 i + 60 j) N
B = (-100 N) (cos(90°) i + sin(90°) j) = (-100 j) N
⇒ A + B = (60√3 i - 40 j) N
⇒ ||A + B|| = √((60√3)² + (-40)²) N = 20√31 N
and its direction relative to the positive horizontal axis (rightward) is θ such that
tan(θ) = (-40) / (60√3) = -2/(3√3)
⇒ θ = arctan(-2/(3√3)) ≈ -21.05°
A Stone is thrown vertically upward with a velocity of Romys A Second Stone is thrown with the same velocity but 1.0 second later. How far apart are the stones when the second one has risen for 3.0 seconds?
Answer: The stones are 34.2 meters apart when the second stone has risen for 3.0 seconds.
Explanation:
The vertical motion of the stones can be described by the equation:
y = y0 + v0t - 0.5gt^2
where y is the height of the stone, y0 is the initial height (which is 0 for both stones since they are thrown from the ground), v0 is the initial velocity, t is the time, and g is the acceleration due to gravity (9.8 m/s^2).
We can solve for the height of the first stone at t = 3 s and the height of the second stone at t = 4 s, and then subtract these two values to find the distance between the stones.
The height of the first stone at t = 3 s is:
y1 = 0 + v0 * 3 - 0.5 * 9.8 * (3^2)
= 0 + v0 * 3 - 4.9 * 9
= 0 + 3v0 - 44.2
The height of the second stone at t = 4 s is:
y2 = 0 + v0 * 4 - 0.5 * 9.8 * (4^2)
= 0 + v0 * 4 - 4.9 * 16
= 0 + 4v0 - 78.4
The distance between the stones at this time is:
y2 - y1 = (4v0 - 78.4) - (3v0 - 44.2)
= v0 - 34.2
Thus, the stones are 34.2 meters apart when the second stone has risen for 3.0 seconds.
a 1,200 kg car travels at 20 m/s. what is it’s momentum ?
Answer:
24000 kg·m/s
Explanation:
Momentum is Mass x Velocity, so 1200 kg time 20 m/s = 24000 kg-ms/s
The momentum of the car is 24000 Kg•m/s
Momentum is defined as the product of mass and velocity. Mathematically, it can be expressed as:
Momentum = mass × velocity
With the above formula, we can obtain the momentum of the car as follow:
Mass = 1200 KgVelocity = 20 m/sMomentum =?Momentum = mass × velocity
Momentum = 1200 × 20
Momentum of car = 24000 Kg•m/s
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Tectonic plates are large segments of the Earth's crust that move slowly. Suppose one such plate has an average speed of 8.8 cm per year. (a) What distance does it move in 35 seconds at this speed (note that your answer should be in meters while your given speed is in cm/year)? (b) How many miles will the plate move in one million years at this speed?
Answer:
Jun 29, 2016 · Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1.0 s at this speed? (b) What is its speed in kilometers per million years?
Explanation:
Does anyone know how to work this out?
Answer:
\(\frac{17}{14}*5\) = Approximately 6
Explanation:
What we need to know:
1. Given that this is a parallel circuit, each pathway will receive the full voltage from the source. Therefore, each pathway will receive 17V.
2. The current (I) stays the same for all loads in series. Therefore, I2 and I3 are equal since they are connected in series.
3. Ohm's law states that Voltage = Current × Resistance (V=IR)(I=V/R)(R=V/I)
1) Calculate the current for the path containing R2 and R3
\(I_2_,_3=\frac{V_2_,_3}{R_2_,_3}\\I_2_,_3=\frac{17}{5+9}\\I_2_,_3=\frac{17}{14}\)
Because the current running through this path is \(\frac{17}{14}\) A, then I2 is \(\frac{17}{14}\) A.
2) Use Ohm's Law by plugging in I2 and R2
\(V_2=I_2*R_2\\V_2=\frac{17}{14} *5\)
\(V_2=6\) (approximate)
Therefore, V2 is approximately 6V.
I hope this helps!
An elevator is moving with an acceleration of 2.5 m/s. Find the tension in the cables if the total mass of a man and elevator is 80kg. When;
a) Moving up
b) Moving down
The tension in the cables are : a) 984 N when moving up,
b) 584 N when movng down
Given data:
mass = 80 kg
Acceleration = 2.5 m/s
Determine the tension in the cablesA) When moving up
Tension in the cable = m*g + m*a
= 80 * 9.8 + 80 * 2.5
= 984 N
B) When moving down
Tension in the cable = m*g - m*a
= 80 * 9.8 - 80 * 2.5
= 584 N
Hence we can conclude that the tension in the cable are 984 N moving up and 584 moving down.
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1. Compare the slope of the distance vs. time graph to the average of all your velocity values. Are they close? Why or why not? What does the slope of a distance (or displacement) vs. time graph mean? Explain the answer using your data and include your Distance vs. Time graph and a chart of distance, time, and average velocity.
The slope of the distance vs. time graph and the average of all the velocity values should be close, as the slope of the distance vs. time graph represents the average velocity. If the motion is uniform, the slope will be constant and equal to the average velocity. However, if the motion is not uniform, the slope will vary, resulting in a deviation from the average velocity.
The slope of a distance (or displacement) vs. time graph represents the rate of change of distance with respect to time, which is the velocity. In other words, the slope indicates how fast an object is moving. If the motion is uniform (constant velocity), the slope remains constant, and its value is equal to the average velocity.To compare the slope of the distance vs. time graph with the average velocity, we need to analyze the data and calculate the average velocity.Analyze the given data and plot the Distance vs. Time graph using the provided distance and time values.Calculate the average velocity by dividing the total distance traveled by the total time taken. Use the given distance and time values to obtain the individual velocities and then find their average.Compare the slope of the distance vs. time graph to the calculated average velocity. If the motion is uniform, the values should be close.Explain the result: If the motion is uniform, the slope and the average velocity will be close since the slope represents the average velocity. However, if the motion is not uniform, the slope will vary at different points, resulting in a deviation from the average velocity.Include the Distance vs. Time graph and a chart of distance, time, and average velocity to visualize the data and support the explanation.By analyzing the data and comparing the slope of the distance vs. time graph to the average velocity, you can determine the consistency of the motion and the relationship between the two values.For more such questions on slope , click on:
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if the rest of the solar system were to disappear, the moon would
Answer:
Of course the moon would disappear
Explanation:
The Moon is part of the solar system.
A 200 W engine generates 4000 J of energy. How long did it run for?
A. 20 s
B. 200 s
C. 0.2 s
D. 2 s
Answer:
A
Explanation:
power = energy/time
200 = energy / t
200 = 4000/t
t = 4000/200= 20 sec
2. A girl and her bicycle have a total mass of 40 kg. At the top of the hill her speed is 5.0 m/s.
The hill is 10 m high and 100 m long.
If the magnitude of the force of friction as she rides down the hill is 20 N, what is her speed
at the bottom of the hill? (Take g=9.8 m/s?)
(a) 5.0 m/s
(b) 10 m/s
(c) 11 m/s
(d) 18 m/s
(e) She stops before she reaches the bottom.
Answer:
Explanation:
1. First draw a free body diagram of the scenerio (a block sliding down a a slant surface).
2. Then we analyze the forces and write equations that satisfy Fnet = ma. This will give us the acceleration as the block slides down the surface.
3. Last, we can use the kinematic equation (vf^2 = vi^2 + 2as) and to solve the final speed of the block.
Particles q₁ +8.0 μC, q2 +3.5 μC, and
93-2.5 μC are in a line. Particles q₁ and q2 are
separated by 0.10 m and particles q2 and q3 are
separated by 0.15 m. What is the net force on
particle q₂?
Remember: Negative forces (-F) will point Left
Positive forces (+F) will point Right
+8.0μ.C
+91
0.10 m
+3.5 C
+92
0.15 m
-2.5μ C
93
The net force on particle q₂, located between particles q₁ and q₃, is approximately 189000 N. The force exerted by particle q₁ on q₂ is positive and equals 252000 N, while the force exerted by particle q₃ on q₂ is negative and equals -63000 N.
To find the net force on particle q₂, we need to calculate the individual forces exerted on q₂ by particles q₁ and q₃ and then determine their sum.
The force between two charged particles can be calculated using Coulomb's law:
F = k * |q₁ * q₂| / r²
Where F is the force between the particles, k is the electrostatic constant (k ≈ 9.0 x \(10^9\) Nm²/C²), q₁ and q₂ are the charges of the particles, and r is the distance between them.
First, let's calculate the force exerted on q₂ by q₁:
F₁₂ = k * |q₁ * q₂| / r₁₂²
F₁₂ = (9.0 x \(10^9\) Nm²/C²) * |(8.0 μC) * (3.5 μC)| / (0.10 m)²
F₁₂ ≈ 252000 N
The force is positive because q₁ and q₂ have opposite charges.
Next, let's calculate the force exerted on q₂ by q₃:
F₂₃ = k * |q₂ * q₃| / r₂₃²
F₂₃ = (9.0 x \(10^9\)Nm²/C²) * |(3.5 μC) * (-2.5 μC)| / (0.15 m)²
F₂₃ ≈ -63000 N
The force is negative because q₂ and q₃ have the same charge.
Finally, we can find the net force on q₂ by summing the individual forces:
Net force = F₁₂ + F₂₃
Net force = 252000 N + (-63000 N)
Net force ≈ 189000 N
The net force on particle q₂ is approximately 189000 N.
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The turn signal belongs to which subsystem of an automobile?
A.
transmission
B.
fuel
C.
suspension
D.
control
The turn signal belongs to the control subsystem of an automobile.
What turn signal ?Turn signals serves as the control that help motorists to react and plan for road user making a turn in front of them.
This is part of the subsystem of an automobile. which help to maintain the best driving experience on the road.
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a. When throwing a ball vertically upward, my hand moves through a distance of about 1.0 m before the ball leaves my hand. The 0.80 kg ball reaches a maximum height of about 20 m above my hand. while the ball is in my hand after the ball leaves my hand
The required, it experiences a downward force due to gravity and a force due to air resistance.
What is the projectile motion?Projectile motion is the movement of an entity projected into space. After the initial force that launches the object, it only experiences the force of gravity. The object is called a projectile, and its path is called its trajectory.
Here,
When throwing a ball vertically upward, there is a displacement of about 1.0 m from the initial position of the hand to the position where the ball leaves the hand. The mass of the ball is 0.80 kg and it reaches a maximum height of about 20 m above the initial position of the hand. While the ball is in the hand after it leaves, it experiences a downward force due to gravity and a force due to air resistance.
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Explain how energy can escape from the water by convection,
As the molecules at the surface of a liquid absorb heat, they begin to move around more quickly. This gives them the energy to break the bonds that connect them to other water molecules. When the molecules are moving fast enough, they are able to "escape." They leave the surface of the liquid as gas molecules.
A student sits on a rotating stool holding two 3.6-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg · m2 and is assumed to be constant. The student then pulls in the objects horizontally to 0.43 m from the rotation axis. (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the student before and after the objects are pulled in. before J after J
(a) The new angular speed of the student is 2.34 rad/s, and (b) The kinetic energy of the student before the objects are pulled in is 8.22 J, and the kinetic energy of the student after the objects are pulled in is 24.8 J.
Angular speed, also known as rotational speed, is the measure of how fast an object rotates or revolves around a central point or axis, and it is measured in radians per second (rad/s) or degrees per second (°/s). It is a scalar quantity that describes the magnitude of the rotational velocity of an object.
(a) To solve for the new angular speed of the student, we can use the conservation of angular momentum. Initially, the student, stool, and objects have an angular momentum given by:
L = Iω
where I is the moment of inertia and ω is the angular speed. Since there is no external torque acting on the system, the angular momentum is conserved. Therefore, we can write:
I1ω1 = I2ω2
where I1 and ω1 are the initial moment of inertia and angular speed, and I2 and ω2 are the final moment of inertia and angular speed.
At the initial state, the moment of inertia of the student plus stool and objects is given by:
I1 = I_student + I_objects
where I_student is the moment of inertia of the student and stool and I_objects is the moment of inertia of the objects. The moment of inertia of the objects can be approximated as:
I_objects ≈ 2mr²
where m is the mass of one object and r is the distance from the axis of rotation to the object. Substituting the given values, we get:
I1 = 3.0 kg·m² + 2(3.6 kg)(1.0 m)² ≈ 29.04 kg·m²
At the final state, the moment of inertia is given by:
I2 = I_student + 2mr²
where r is the new distance from the axis of rotation to the objects. Substituting the given values, we get:
I2 = 3.0 kg·m² + 2(3.6 kg)(0.43 m)² ≈ 8.97 kg·m²
Substituting the known values and solving for ω2, we get:
I1ω1 = I2ω2
(29.04 kg·m²)(0.75 rad/s) = (8.97 kg·m²)ω2
ω2 ≈ 2.34 rad/s
So, the new angular speed of the student is approximately 2.34 rad/s.
(b) To solve for the kinetic energy of the student before and after the objects are pulled in, we can use the formula:
KE = (1/2)Iω²
where KE is the kinetic energy, I is the moment of inertia, and ω is the angular speed.
At the initial state, the kinetic energy is given by:
KE1 = (1/2)I1ω1² ≈ 8.22 J
Substituting the known values, we get:
KE1 ≈ (1/2)(29.04 kg·m²)(0.75 rad/s)² ≈ 8.22 J
At the final state, the kinetic energy is given by:
KE2 = (1/2)I2ω2²
Substituting the known values, we get:
KE2 ≈ (1/2)(8.97 kg·m²)(2.34 rad/s)² ≈ 24.8 J
So, the kinetic energy of the student before the objects are pulled in is approximately 8.22 J, and the kinetic energy of the student after the objects are pulled in is approximately 24.8 J.
Therefore, (a) The student's new angular speed is 2.34 rad/s, and (b) the student's kinetic energy before the objects are drawn in is around 8.22 J, and the student's kinetic energy after the things are pushed in is roughly 24.8 J.
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A spring has a spring constant of 450 N/m. How much must this spring be stretched to store 49 J of potential energy?
Answer:
W = 1/2 K x^2
x^2 = 2 * W / K = 2 * 49 J / (N/m) = .218 / m^2
x = .467 m
what are the applications of triangle law of forces
Answer:
The triangle law of forces can also be stated as. if a body is in equilibrium under the action of three forces acting at a point, then the three forces can be completely represented by the three sides of a triangle taken in order. A body might be subjected to further than one force at a similar time.
Explanation:
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