For an uniformly accelerated motion, the following relationship is used:
[tex]2 a S=v_f^2 -v_i ^2[/tex] (1)
where a is the acceleration, S the distance covered, and vf and vi the final and initial speeds of the motion.
In our problem we are dealing with a rotational motion. Initially, the salad spinner has constant angular speed, which is given by
[tex]\omega _i = 2 \pi f[/tex]
where f is the rotational frequency, which is the number of revolutions per second:
[tex]f= \frac{20 rev}{5 s}=4 Hz [/tex]
so the initial angular speed is
[tex]\omega _i = 2 \pi (4 Hz)=25.2 rad/s[/tex]
Then, the salad spinner starts to decelerate with constant deceleration [tex]\alpha[/tex], and during its deceleration it spins for other 6 revolutions, so covering a total angle of
[tex]\theta = 2 \pi (6 rev)=37.7 rad[/tex]
until it stops, so until it reaches a final speed of [tex]\omega _f=0[/tex].
To find the angular acceleration, we can use the equivalent of equation (1) for angular motions:
[tex]2 \alpha \theta = \omega_f^2 - \omega_i^2[/tex]
and so, since the final speed is [tex]\omega _f=0[/tex]:
[tex]\alpha = - \frac{\omega _i^2}{2 \theta}=- \frac{(25.2 rad/s)^2}{2\cdot 37.7 rad}=-8.4 rad/s^2 [/tex]
where the negative sign means the salad spinner is decelerating.
Answer:
[tex] \alpha = -\frac{(25.132 rad/s)^2}{2* 37.7 rad}= -8.377 rad/s^2[/tex]
And we can convert this into degrees like this:
[tex] \alpha= -8.377 rad/s^2 * (\frac{180}{\pi rad}) =-479.967 rad/s^2[/tex]
Explanation:
For this case we assume that the angular acceleration is constant and the spinner slows down and come to rest at the end
We can calculate the distance traveled each revolution with this formula:
[tex] \theta= 20 rev * \frac{2\pi rad}{1 rev}= 40 \pi rad[/tex]
And since we know that the time to reach the velocity 0 is 5 s we can find the angular velocity like this:
[tex] w_o= \frac{\theta}{t}= \frac{40 \pi rad}{5 s}= 25.132 rad/s[/tex]
We know that the spinner rotates 6 more times before come rest, so the total distance traveled is:
[tex] \theta= 6* 2\pi = 37.699 rad[/tex]
[tex] w_f = 0 rad/s[/tex]
And we have the following formula :
[tex] w^2_f = w^2_i + 2\alpha \theta[/tex]
Since we know that the final angular velocity is 0 we can solve for [tex] \alpha[/tex] the angular acceleration and we got:
[tex] \alpha = -\frac{w^2_o}{2 \theta}[/tex]
And replacing the values that we found before we have this:
[tex] \alpha = -\frac{(25.132 rad/s)^2}{2* 37.7 rad}= -8.377 rad/s^2[/tex]
And we can convert this into degrees like this:
[tex] \alpha= -8.377 rad/s^2 * (\frac{180}{\pi rad}) =-479.967 rad/s^2[/tex]
Why are objects that fall near Earth’s surface rarely in free fall?
Gravity does not act on objects near Earth’s surface.
Air exerts forces on falling objects near Earth’s surface.
The objects do not reach terminal velocity.
The objects can be pushed upward by gravity.
An unmanned spacecraft leaves for Venus. Which statements about the spacecrafts journey are true?
A)The weight of the spacecraft keeps changing.
B)The mass of the spacecraft keeps changing
C)The weight of the spacecraft remains the same
D) The mass of the spacecraft remains the same
E)The gravotational pull on the spacecraft remains the same
Hint: There is more than one answer
Answer:
A)The weight of the spacecraft keeps changing.
D) The mass of the spacecraft remains the same
Explanation:
As we know that the acceleration due to gravity depends on the height from the surface
As we know that the force due to gravity on objects near the surface is given as
[tex]F = \frac{Gm_1m_2}{(R+h)^2}[/tex]
here we know that
R = radius of planet
h = height from the surface of planet
So as we move away at more height the gravitational attraction force will keep on decreasing.
This gravitational attraction force of planet is also known as weight so we can say that the weight of the object will keep on changing while object move away.
Also we know that mass of object is quantity of the matter which always remains constant.
What is the maximum velocity for the pacific plate?
One side of the moon always faces Earth because the time it takes the moon to spin on its axis is blank the time it takes the moon to travel around Earth.
Answer: One side of the moon always faces Earth because the time it takes the moon to spin on its axis is "the same as" the time it takes the moon to travel around Earth.
Dr. Lao has discovered a substance that emits energy in the form of waves. If Dr. Lao observes that these waves can travel through a perfect vacuum, then
Answer: The waves that travel through vacuum is electromagnetic waves.
Explanation:
There are two types of waves:
Mechanical waves: These are the waves that need a medium to travel so that they can transport their energy from one location to another. For Example: Sound waves
Electromagnetic waves: These are waves which can travel through vacuum. These have electrical and magnetic component associated with them. They travel with the speed of light. They does not require a medium to travel. For Example: Infrared waves, Microwaves
Hence, the waves that travel through vacuum is electromagnetic waves.
"why might a good electrical conductor also be a good thermal conductor"
A stone is thrown outward from the top of a 59.4-m high cliff with an upward velocity component of 19.5 m/s. how long is stone in the air?
The stone is in the air for 6 seconds.
[tex]\texttt{ }[/tex]
Further explanationAcceleration is rate of change of velocity.
[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]
[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]
a = acceleration ( m/s² )
v = final velocity ( m/s )
u = initial velocity ( m/s )
t = time taken ( s )
d = distance ( m )
Let us now tackle the problem!
[tex]\texttt{ }[/tex]
Given:
height of the cliff = h = 59.4 m
speed of the stone = u = 19.5 m/s
Asked:
total time taken = t = ?
Solution:
[tex]h = ut + \frac{1}{2}at^2[/tex]
[tex]-59.4 = 19.5t - \frac{1}{2}(9.8)t^2[/tex]
[tex]-59.4 = 19.5t - 4.9t^2[/tex]
[tex]49t^2 -195t - 594 = 0[/tex]
[tex]( t - 6 ) ( 49t + 99 ) = 0[/tex]
[tex]t - 6 = 0[/tex]
[tex]t = 6 \texttt{ s}[/tex]
[tex]\texttt{ }[/tex]
Learn moreVelocity of Runner : https://brainly.com/question/3813437Kinetic Energy : https://brainly.com/question/692781Acceleration : https://brainly.com/question/2283922The Speed of Car : https://brainly.com/question/568302[tex]\texttt{ }[/tex]
Answer detailsGrade: High School
Subject: Physics
Chapter: Kinematics
[tex]\texttt{ }[/tex]
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Projectile , Motion , Horizontal , Vertical , Release , Point , Ball , Wall
A stone is thrown outward from the top of a 59.4-m high cliff with an upward velocity component of 19.5 m/s. The stone is in the air for 6 seconds.
What is acceleration?The rate at which an item changes its velocity is known as acceleration, a vector quantity. If an object's velocity is changing, it is acceleration.
Given in the question a stone is thrown outward from the top of a 59.4-m high cliff with an upward velocity component of 19.5 m/s.
Acceleration is rate of change of velocity.
a = acceleration ( m/s² )
v = final velocity ( m/s )
u = initial velocity ( m/s )
t = time taken ( s )
d = distance ( m )
height of the cliff = h = 59.4 m
speed of the stone = u = 19.5 m/s
to find total time taken = t = ?
s = ut + 1/2 at² putting the value we get,
t = 6 sec
The stone is in the air for 6 seconds.
To learn more about acceleration refer to the link:
brainly.com/question/12550364
#SPJ5
A piano tuner stretches a steel piano wire with a tension of 765 n. the steel wire has a length of 0.700 m and a mass of 5.25 g . part a what is the frequency f1 of the string's fundamental mode of vibration?
The fundamental frequency of the steel piano wire, subjected to a tension of 765 N, with a length of 0.700 m, and a mass of 5.25 g, is approximately 424.6 Hz.
Explanation:The frequency f1 of the string's fundamental mode of vibration can be calculated using the formula f = sqrt(T / μ) / 2L. Here:
T is the tension in the string, which is 765 Nμ is the linear density of the string, which is the mass of the string divided by its length. Therefore, μ = (5.25 g) / (0.700 m) = 0.0075 kg/mL is the length of the string, which is 0.700 mPlugging these values into the formula, we get:
f1 = sqrt((765 N) / (0.0075 kg/m)) / (2 * 0.700 m) = 424.6 Hz
This means that the fundamental frequency of the string is roughly 424.6 Hz.
Learn more about Fundamental Frequency here:https://brainly.com/question/31314205
#SPJ3
Using a crowbar, a person can remove a nail by exerting little force, whereas pulling directly on the nail requires a large force to remove it (you probably can't). why?
Final answer:
Using a crowbar to remove a nail requires less force because it uses leverage to amplify the input force and increase the mechanical advantage.
Explanation:
When using a crowbar to remove a nail, you are using a lever with a large mechanical advantage. The input force you apply to the crowbar is much smaller than the force exerted by the crowbar on the nail. This is because the length of the crowbar provides a greater lever arm, which increases the mechanical advantage.
On the other hand, when you try to pull directly on the nail, you don't have the same leverage as the crowbar, so you need to exert a larger force to overcome the resistance of the nail.
In summary, the crowbar allows you to remove a nail with less force because it uses leverage to amplify the input force and increase the mechanical advantage.
Which of the following occurs over a resistor in a circuit? Current is dissipated. Voltage is dropped. Charge is stored. Electrical energy is stored.
In a circuit, a voltage drop occurs over a resistor as the electric current flows through it, transforming electrical energy into heat due to resistance, not storing charge or electrical energy. the correct answer is voltage is dropped.
Among the choices provided for what occurs over a resistor in a circuit, the correct answer is voltage is dropped. When electric current flows through a resistor, it encounters resistance which impedes the flow of charge. This results in a voltage drop across the resistor. The energy that the charges lose as they pass through the resistor is dissipated mainly in the form of heat. This concept is reflected in the equation for electric power dissipation, P = IV, where P represents power, I is current, and V is voltage. This can also be expressed as P = I²R or P = V²/R using Ohm's law, where R is the resistance. Contrary to some of the other choices, resistors do not store charge or electrical energy; that function is typically carried out by capacitors in a circuit.
500 ml of four different liquids are heated to 50oC. According to the specific heat data, which liquid will cool to 35oC in the shortest amount of time?
Answer:C) gasoline
Explanation:
Specific heat is the measure of the heat energy required to increase or decrease the temperature of a substance by a certain temperature interval. Gasoline has the lowest specific heat; that means it takes less energy to lower or raise the temperature of gasoline compared to the other three liquids.
why were you able to see the effects of the magnetic fields using iron filings
HELP PLEASE!! ASAP
Which accurately compares concave and convex lenses?
A. With both concave and convex lenses, the characteristics of the image do not depend on the placement of the object.
B. With both concave and convex lenses, the characteristics of the image depend on the placement of the object.
C. With concave lenses, the characteristics of the image do not depend on the placement of the object, but with convex lenses, they do.
D. With convex lenses, the characteristics of the image do not depend on the placement of the object, but with concave lenses, they do.
With concave lenses, the characteristics of the image do not depend on the placement of the object, but with convex lenses, they do.
A wave is a disturbance that carries from one place to another through matter and space.
Answer:
Energy
Explanation:
Eng 2021
A mass of 15 kg of air in a piston-cylinder device is heated from 25 to 77°c by passing current through a resis tance heater inside the cylinder. the pressure inside the cylin der is held constant at 300 kpa during the process, and a heat loss of 60 kj occurs. determine the electric energy supplied, in kwh
When a guitar string plays the note "a," the string vibrates at 440 hz ?
Answer:
440hz
Explanation: Guitars do in fact play at 440 herts for the note a
A charge of 7.2 × 10-5 C is placed in an electric field with a strength of 4.8 × 105. If the electric potential energy of the charge is 75 J, what is the distance between the charge and the source of the electric field? Round your answer to the nearest tenth.
The distance between the charge and the source of the electric field is 2.2 m.
The potential energy U of a charge q placed in an electric field created by a source charge Q, at a distance r from the source charge is given by,
[tex] U=\frac{kQq}{r} [/tex] ...... (1)
Here, k is the Coulomb constant.
The electric field E at a distance r from the source charge is given by,
[tex] E =\frac{kQ}{r^2} [/tex] ......(2)
From equations (1) and (2)
[tex] U=E*q*r [/tex]
Rewrite the expression for ri.
[tex] r=\frac{U}{Eq} [/tex]
Substitute 75 J for U, [tex] 4.5*10^5 V/m [/tex] for E and [tex] 7.5*10^{-5} C [/tex] for q.
[tex] r=\frac{U}{Eq} \\ =\frac{75 J}{(4.8*10^{5} V/m)(7.2*10^{-5}C)} \\ =2.17 m [/tex]
Rounding off to the nearest tenth, the the distance between the charge and the source charge is 2.2 m
In terms of the torque needed to rotate your leg as you run, would it be better to have a long calf and short thigh or vice versa? a) Long calf, short thigh b) Short calf, long thigh c) Does not matter
Having a short calf and long thigh would result in better torque for leg rotation during running, as a longer lever arm (thigh) from the pivot point (knee) allows for greater torque. However, proportions should be balanced for optimal running biomechanics.
Explanation:In terms of the torque needed to rotate your leg as you run, it would be better to have a short calf and long thigh. This is because torque is the rotational equivalent of force and is calculated by multiplying the force by the distance from the pivot point. In this case, the pivot point is the knee.
Therefore, a longer thigh would result in a greater torque because the force (muscle contraction) is applied further from the pivot point (knee). Conversely, a short calf means less mass is being rotated around the pivot point, reducing the torque needed for movement.
Learn more about torque here:https://brainly.com/question/25708791
#SPJ11
In terms of the torque needed to rotate your leg as you run, it be better to have b) Short calf, long thigh
In terms of the torque needed to rotate your leg as you run, it would be better to have a short calf and long thigh.
This is because torque is the rotational equivalent of force, and it depends on both the magnitude of the force and the distance from the pivot point where the force is applied. In running, the longer the distance from the pivot point (knee), the more torque is generated by the same muscle force. A long thigh and short calf combination helps in maximizing this distance, thereby reducing the effort required to achieve the same angular acceleration of the leg.
Let's break this down step-by-step:
Torque (τ) is defined as τ = r × F, where r is the distance from the pivot point (in this case, the knee) and F is the force applied by the muscles.For a given force, increasing the distance r will increase the torque, making it easier to rotate the leg.A long thigh means a greater r from the hip pivot point, increasing the torque generated for the same muscle effort.A short calf means less weight and less moment of inertia that needs to be rotated, making the rotation more efficient.How much work does an elevator motor do to lift a 1200-kg elevator car a height of 80 m at constant speed?
Answer:
Work = 940800 J
Explanation:
As we know that work done is defined as
Work = (Force)(displacement in the direction of force)
here elevator motor lift a mass of 1200 kg
so in order to lift it up motor must have to apply the force same as the weight so that it will move up with constant speed.
so here we have
[tex]F = mg[/tex]
[tex]F = (1200 kg)(9.8 m/s^2)[/tex]
[tex]F = 11760 N[/tex]
now it is displaced upwards by distance d = 80 m
so here we have
[tex]W = (11760)\times (80)[/tex]
[tex]W = 940800 J[/tex]
so above is the work done by the elevator to lift it upwards
What was the speed of the cannon ball if the spring compressed 58 cm when the cannon was fired?
To calculate the speed of a cannon ball using the distance the spring compressed, the spring constant is required to use energy conservation principles. Without this value, it is not possible to provide an exact answer.
To determine the speed of the cannon ball given that the spring compressed 58 cm when it was fired, we would use the conservation of energy principle where the potential energy stored in the spring is converted into the kinetic energy of the cannon ball. If we had the spring constant (k), we could use the formula for the potential energy stored in a spring, which is PE_spring = (1/2)kx² where x is the compression distance, and equate this to the kinetic energy formula KE = (1/2)mv², where m is the mass of the cannon ball, and v is the velocity we want to find. Without the specific spring constant, it is not possible to calculate the exact speed of the cannon ball.
A proton beam in an accelerator carries a current of 106 μa. if the beam is incident on a target, how many protons strike the target in a period of 17.0 s?
A rocket in orbit just above the atmosphere is moving in uniform circular motion. The radius of the circle in which it moves is 6.381 × 106 m, and its centripetal acceleration is 9.8 m/s2 . What is the speed of the rocket?
If r1 < r2 < r3, and if these resistors are connected in series in a circuit, which one dissipates the most power
If it takes 6.02 kj of heat energy to melt a mole of ice, how much heat is absorbed when 6.30 g of water melts? 21.0 j 2.10 kj 21 kj 0.210 kj
Brass is an alloy of copper and zinc the two metals are melted mixed and then solidified how would you best classify brass
Brass can be classified as [tex]\boxed{{\text{a}}{\text{. homogenous mixture and a solid solution}}}[/tex].
Further explanation:
Alloy:
An alloy is defined as combination of metals or a combination of one or more metals with non-metals. Alloys have a large range of applications, ranging from surgical tools, aerospace industry to automobile construction. Steel, solder, brass, pewter, bronze, and amalgams are some examples of alloys. Alloys can be either solid solution or a mixture of metallic phases.
Mixture:
The material that is made up of two or more substances is called a mixture. It has no fixed formula, and its composition is also varied. All the individual constituents retain their properties after the formation of the mixture.
Types of mixtures:
1. Homogeneous mixtures
Homogeneous is a Latin word that means the same. These mixtures have a uniform composition throughout. Air, orange juice, and blood are the examples of a homogenous mixture.
2. Heterogeneous mixtures
Heterogeneous is a Latin word that means different. These mixtures that have non-uniform composition throughout. Concrete, soda, and chocolate chip cookies are the examples of a heterogeneous mixture.
Characteristics of mixtures:
1. It has a variable composition and has no formula.
2. Mixtures are not formed by any chemical reactions.
3. Mixtures can be either homogeneous or heterogeneous.
4. The constituents of the mixtures can be separated by physical methods such as filtration, heating, drying, distillation, crystallization.
5. The properties of the individual particles of the mixture are retained even after the formation of mixtures.
Copper and zinc are the two metals that are first melted, mixed and then solidified to form brass. Their composition is the same throughout the whole part of brass. So brass is an example of homogeneous mixture. It is also known as solid solution where zinc acts as solute and copper is a solvent.
Learn more:
1. The major contribution of Antoine Lavoisier to chemistry: https://brainly.com/question/2500879
2. Example of physical change: https://brainly.com/question/1119909
Answer details:
Grade: High School
Subject: Chemistry
Chapter: Mixture
Keywords: mixture, characteristics, formula, composition, properties, chemical reactions, filtration, distillation, heating, crystallization, homogeneous, heterogeneous, brass, alloy, metals, non-metals, aerospace industry, automobile construction, surgical tools, solid solution, zinc and copper.
how high was a brick dropped from if if falls in 2.5 seconds?
Which of the following correctly describes the first animals that appeared?
A.) these were large creatures, similar to dinosaurs
B.) these were bony creatures that lived only in wet environments
C.) these were soft and boneless creatures
D.) these were large creatures that lived only in dry environments
Two appliances are connected in parallel to a 120-v battery and draw currents i1 = 3.0 a and i2 = 3.1
a. if these appliances are instead connected in series to the same battery, what is the total current in the circuit?
A cylinder with a moveable piston contains 219 ml of nitrogen gas at a pressure of 1.23 atm and a temperature of 295 k . part a what must the final volume be for the pressure of the gas to be 1.53 atm atm at a temperature of 337 k ?
The final volume needed for the pressure of the nitrogen gas to be 1.53 atm at a temperature of 337 K is approximately 190.8 ml. This is calculated using the combined gas law.
Explanation:To find out what the final volume of nitrogen gas in the cylinder would be when the pressure is 1.53 atm and the temperature is 337 K, we can use the combined gas law, which is derived from the ideal gas law. The combined gas law states that the ratio of the product of pressure and volume to temperature remains constant for a fixed amount of gas when the temperature is measured in Kelvin. The formula for the combined gas law is (P1 * V1) / T1 = (P2 * V2) / T2, where P is pressure, V is volume, and T is temperature.
Given that:
Initial pressure (P1) = 1.23 atmInitial volume (V1) = 219 mlInitial temperature (T1) = 295 KFinal pressure (P2) = 1.53 atmFinal temperature (T2) = 337 KWe want to find the final volume (V2), so rearranging the equation to solve for V2 gives us:
V2 = (P1 * V1 * T2) / (P2 * T1)
Substituting the known values:
V2 = (1.23 atm * 219 ml * 337 K) / (1.53 atm * 295 K)
By performing the calculations:
V2 ≈ 190.8 ml
Therefore, the final volume needed for the pressure of the nitrogen gas to be 1.53 atm at 337 K is approximately 190.8 ml.
Chanel has some cotton candy that came in a cloudy shape. She wants to make it more dense. Which describes the candy before and after Chanel manipulated it?
1)The candy before was a cube, and the candy after was a ball.
2)The candy before was compacted, and the candy after was fluffy.
3)The candy before was fluffy, and the candy after was compacted.
4)The candy before was a ball, and the candy after was a cube.
Answer: Option (C) is the correct answer.
Explanation:
As we known that density is the amount of mass divided by volume of the substance.
Mathematically, Density = [tex]\frac{mass}{volume}[/tex]
So, when candy was present in the shape of a cloud then it means that it was fluffy as it has more volume.
Since, density is inversely proportional to volume therefore, with increase in volume there will occur a decrease in density.
But when the candy will become compact then there will occur a decrease in its volume. Hence, then there will occur an increase in the density of the candy.
Thus, we can conclude that the statement candy before was fluffy, and the candy after was compacted best describes the candy before and after Chanel manipulated it.