the linear speed at 12.0 diameter and angular velocity 34.6rad/s is 2.076m/s and centripetal acceleration is 0.718296m/s².
What is linear speed and centripetal force?The term "linear speed" describes the change in distance as a function of time. This shift could happen overnight or gradually. In contrast to average linear speed, which is defined as linear speed seen over a longer time period, instantaneous linear speed is defined as linear speed recorded over a relatively brief period of time. However, it is more accurate to measure the linear speed over a brief period of time.
A net force that keeps an object moving in a circular motion is known as a centripetal force.
Centripetal acceleration, any item moving along a circular path with a radius of rrr and a velocity of vvv experiences an acceleration that is directed toward the path's centre, with the formula a = frac v2 r a= r v 2.
A equals v squared divided by r, where r is the end fraction.
We need talk about how the object started out travelling in a circular motion, though. According to Newton's first law, unless acted upon by an outside force, an object will continue to move in a straight path. The centripetal force is the outside force in this situation.
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The water displacement method was used to determine the density of silly putty. The initial water level in graduated cylinder was 25 ml and the final water level after placing silly putty into graduated cylinder was 29 ml. The mass of the silly putty was 8 grams. Calculate the density of the silly putty.
Answer:
The density of putty 2 g/cm³
Explanation:
Given:
V₀ = 25 ml = 25 cm³
V = 29 ml = 29 cm³
m = 8 g
______________
ρ - ?
The density of putty:
ρ = m / (V - V₀)
ρ = 8 / (29 - 25) = 8 / 4 = 2 g/cm³
PLEASE HELP CALCULATE THE NET FORCE ON THE BLUE TRIANGLE. THE VALUE OF THE NET FORCE IS BLANK AND THESE FORCES ARE REFERRED TO AS BLANK
show your work . zoom in
The value of the net force is 0 N, and these forces are referred to as balanced forces.
What is net force?The net force of an object is the sum of all the forces acting on object. The net force on an object gives the resultant force on the object.
The net force on an object is given by the sum of all the forces acting on a particular direction, like sum of the upward forces and sum of the horizontal forces.
Mathematically, the formula for net force on an object is given as;
F(net) = Fₓ₁ - Fₓ₂
where;
Fₓ₁ is the first force on the object acting in positive horizontal directionFₓ₂ is the second force on the object acting in a negative horizontal directionF(net) = Fy₁ - Fy₂
Fy₁ is the first force on the object acting in positive vertical directionFy₂ is the second force on the object acting in a negative vertical directionThe net force acting on the object is calculated as follows;
F(net) vertical force = 50 N - 50 N = 0
F(net) vertical force = 30 N - 30 N = 0
Thus, the object is in state of equilibrium since all the forces acting on the object are balanced.
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how do vibrating objects produce sound waves
Answer:
Vibrating objects produce sound waves from pressure waves.
Explanation:
The sound produced is transmitted through pressure waves within the object. The object vibrating back and forth rapidly pushes air foward to make way for itself. When a force is officially applied on an atom, it continues to move from its original position and exerts a force on the adjacent atom.
What type of wave is generated by
moving a fixed rope up and down?
Answer:
transverse waves.
Explanation:
what is the power dissipated in a if it is connected to a 4.00 v battery that has negligible internal resistance?
The power dissipated if the resistor A is connected to a 4.00 V battery that has negligible internal resistance is 1.42 W
According to Ohm's law,
V = IR
V = Voltage
I = Current
R = Resistance
For resistor A,
I1 = 0.5 A
V1 = 2.55 V
R1 = 2.55 / 0.5
R1 = 5.1 Ω
I2 = 1 A
V2 = 3.11 V
R2 = 3.11 / 1
R2 = 3.11 Ω
I3 = 2 A
V3 = 3.77 V
R3 = 3.77 / 2
R3 = 1.885 Ω
I4 = 4 A
V4 = 4.58 V
R4 = 4.58 / 4
R4 = 1.145 Ω
R = ( R1 + R2 + R3 + R4 ) / 4
R = ( 5. + 3.11 + 1.885 + 1.145 ) / 4
R = 2.81 Ω
P = V² / R
P = Power
V = 4 V
P = 4² / 2.81
P = 1.42 W
Therefore, the power dissipated if it is connected to a 4.00 V battery that has negligible internal resistance is 1.42 W
The given question is incomplete. The complete question is:
The voltage drop Vab across each of resistors A and B was measured as a function of the current I in the resistor. The results are shown in the table attached. What is the power dissipated in A if it is connected to a 4.00 V battery that has negligible internal resistance?
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protostars are select an answer and submit. for keyboard navigation, use the up/down arrow keys to select an answer. a far less bright than our sun because of their low temperatures. b about as bright as a typical star such as our sun. c far brighter than typical stars because of their large surface area. d essentially invisible and almost impossible to detect.
The correct answer is option C.
Protostars are far brighter than typical stars because of their large surface area.
Generally, newly born stars or young stars are called protostars.
In other words, protostars are characterized as giant balls or clouds of dust and gases which gradually transform into a star over the years.
These stars have very large surface area at their early stage of formation because they keep collecting gaseous cloudy mass from their parent star due to their huge mass and large surface area.
Most protostars are going through their early phase evolution called stellar evolution.
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When heat is added to a system, it goes into which of the following?a.)doing work and/or increasing the internal energyb.)adding to the internal energy only c.)doing work only
ANSWER
b. adding to the internal energy only
EXPLANATION
The 1st Law of Thermodynamics states that the total change in the internal energy of a system, ΔU, is equal to the sum of the net heat transfer into the system, Q, and the net work done on the system, W,
[tex]\Delta U=Q+W[/tex]As we can see in this equation, we can increase the internal energy of a system by adding heat to the system or doing work to the system.
So, if heat is added to a system it will increase the internal energy of the system.
Hence, the heat goes into adding to the internal energy only.
There are 3.0 amps of current flowing through a 12 volt battery in a circuit. How many amps will flow through the circuit if the resistance in the circuit is reduced by half? A) 1.5 amps B) 3.0 amps C) 6.0 amps D) 12 amps
Answer:
I don't know how to get answer of this question
According to Ohm's law the current through circuit increases when resistance decreases. Thus as the resistance decreased to half, the current doubles from 3 A to 6A. Hence, option C is correct.
What is Ohm's law?Ohm's law states that, potential difference or voltage through a circuit is the product of current and resistance through the circuit. Hence, voltage is directly proportional to both current and resistance.
According to this law, V = IR. Thus, as resistance increases current decreases. It is given that the voltage is 12 V and current though a circuit is 3A, resistance will be 12/3 = 4 Ω.
If resistance reduces to half, that is to 2 Ω, then current will be
V/R = 12 / 2Ω = 6A.
Therefore, when resistance decreases to half, current will doubles . Hence, option C is correct.
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a strong spring is stretched 10 cm by a suspended block. if the block's weight is doubled, the spring will stretch to group of answer choices 5 cm. 10 cm. 15 cm. 20 cm.
Using the concepts of spring, we got that the spring will stretch to d) 20 cm if the block's weight on the strong spring is doubled.
When a block is attached on the spring ,a tension will generate on the spring which actually helps the block to remain suspended with the string.
Gravity tries to attract the block towards the surface and tension tries to remain the block with the spring. When the weight is doubled, to hold the same block on the spring, more tension will generate. Due to that spring will expand further more in downward direction.
So when weight is doubled, then spring will be expanded by another 10cm means total length of expansion of string will be 20cm.
Hence, for a strong spring is stretched 10 cm by a suspended block. if the block's weight is doubled, the spring will stretch to d)20cm
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a convex mirror has a focal length of 13 cm. you place a 6 cm diameter lightbulb 60.0cm from that mirror. what is the lightbulb
The focal length of a convex mirror is about 13.0 cm. A 6.0cm-diameter lamp is positioned 60.0cm away from the mirror.
How do you figure out the convex mirror's image distance?The virtual image created by a convex mirror is always projected behind the mirror, hence the image's distance will always be negative.
How do you calculate a convex mirror's focal length?The formula for calculating the mirror's focal length is f = R/2, where f is its focal length and R is its radius of curvature.
What is the convex formula?Convex lens: A convex lens is a type of lens that focuses light rays that are parallel to its main axis.
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How much energy is in the elastic potential energy store of a spring with a spring constant of 4 N/m if it is stretched from 1 m to 1.1 m in length?
Answer:
0.02 JExplanation:
In order to find the energy in the elastic potential energy store of the spring we use the formula
[tex]U = \frac{1}{2} k Δ {x}^{2} \\ [/tex]
where
U is the elastic potential energy in Joules
k is the spring constant in N/m
Δx is the deformation(stretch or compression) of the spring in metres
from the question
k = 4 N/m
Δx = 1.1 m - 1 m = 0.1 m
We have
[tex]U = \frac{1}{2} \times 4 \times ( {0.1})^{2} \\ = 2 \times 0.01 \\ = 0.02[/tex]
We have the final answer as
0.02 JHope this helps you
There is an elephant shaped weather vane at the top of a corn dryer tower that is 45 m high. If the weather vane weighs 190 N, what is the Potential Energy that the weather vane has?Potential Energy = Weight x HeightWeight = Potential Energy / HeightHeight = Potential Energy / WeightWeight = Mass x 10Mass = Weight / 10
Given,
The weight, W = 190 N
The height, H = 45 m
The potential energy is calculated by the formula,
[tex]PE=\text{Weight}\times Height[/tex]Calculate the potential energy by substituting the given values.
[tex]\begin{gathered} PE=190\text{ N}\times45\text{ m} \\ PE=8,550\text{ J} \end{gathered}[/tex]Thus, the potential energy is 8,550 Joules.
List 3 properties of waves
Answer:
1.wavelength
Explanation:
2. Frequency
3.Speed
4.Amplitude
Answer:
Wave is the propagation of disturbance from one place to another in an organised manner. Waves can be mechanical waves or non-mechanical waves. Mechanical waves like sound waves, require a medium to propagate. While electromagnetic waves are non-mechanical waves that do not require a medium and can travel through a vacuum.
If the particles of the medium move in a direction perpendicular to the wave propagation then the waves are called transverse waves. Longitudinal waves are waves in which the particles of the medium vibrate parallel to the direction of wave propagation.
5 Important Properties of Waves
The main properties of waves are as follows –
Property 1:Amplitude
The maximum displacement of the wave from the mean position is called the amplitude of the wave. It is the maximum height from the centre line to the crest or the trough. The crest is the highest point of the wave and the trough is the lowest point of the wave. Amplitude is measured in metres.
Property 2: Frequency
The number of vibrations passing a fixed point in a given amount of time is called frequency. The unit of frequency is Hertz.
Property 3: Wavelength
Wavelength is the distance between two identical points (adjacent crests or troughs). It is measured in metres. Frequency and wavelength are inversely proportional to each other.
Property 4: Time Period
The time taken by a complete wave to pass through a particular point is called the time period. The time period is measured in seconds. The time period is the reciprocal of the frequency.
Property 5: Speed
For a wave, speed is the distance travelled by a particular point on the wave in the given interval of time. Speed is measured in metres per second.
If the gravity of the moon is 1/6 of Earth’s gravity, what is the mass of an object that has a weight of 115N on the moon?
Answer:
70.3 kg
Explanation:
The MASS will be the same on the moon as on earth....but the eight is different
gravity of moon = gravity of earth/6 = 9.81 / 6 m/s^2
F = ma
F/a = m = 115 N / ( 9.81/6 m/s^2) = 70.3 kg mass
Answer:
Explanation:
Given:
g = 9.8 m/s²
g₁ = g / 6 = 9.8 / 6 ≈ 1.6 m/s²
F = 115 N
____________
m - ?
m = F / g₁
m = 115 / 1,6 ≈ 71.9 kg
a freight train, traveling at a speed of 60km/h, passes a light post over the course of 30 seconds. what is the lenght of the train
In the space of 30 seconds, a freight train moving at 60 km/h passes a light post. The train is 500 meters long.
Explain about the Speed?The first person to calculate speed by accounting for both the distance travelled and the amount of time required was the Italian physicist Galileo Galilei. Galileo described speed as the distance travelled in a unit of time.
The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined.
Miles per hour (mph), kilometers per hour (km/h), and meters per second (m/s) are the three most popular speed units (mph). The distance an object covers in a given amount of time is its speed. Speed equals distance x time is the speed equation.
Speed is 60x (5/18) m/s, or 50/3 m/s, and time is 30 seconds. Distance (train length) = speed x time = 50/3 m/s x 30 s = 500 m.
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The formula shown below is used to calculate the energy released when a specific quantity of fuel is burned. What is the missing factor?
The formula used to calculate the energy released when a specific quantity of fuel is burned is Q = m × c × ΔT
We can use the specific heat formula to determine the amount of energy needed to increase the temperature of a known mass of a substance:
Q = m × c × ΔT
In the specific heat formula, Q stands for the energy transferred in joules, m for the mass of the substances in kilograms, c for the specific heat capacity in J/kg degrees C, and T for the temperature change in degrees Celsius.
The relationship between heat energy and temperature is varied in different materials, and specific heat describes how they interact. When heat energy is supplied to a substance, the temperature will vary by a certain amount.
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It takes a time t = 0.69 s for a record to revolve on a record player once. a particular point on the record moves past the needle at a speed of vn = 0.93 m/s.
The radius at which the needle is in contact moves with a velocity of 0.93 m/s and the time taken 0.69 seconds is 0.102 meters.
What is Speed?Speed is a unit used to describe how quickly an object is moving. The fact that speed is a scalar denotes that it is a measurement with a magnitude but no direction.
A thing that moves swiftly and quickly, moving a great distance in a short period of time. On the other hand, an object moving slowly and moving at a low speed travels a relatively short distance in the same amount of time. Nothing moves at all when an object has no speed.
Given:
The time, t = 0.69 seconds,
The speed, s = 0.93 m/s,
Calculate the distance covered by the needle,
d = [tex]s*t[/tex]
Substitute the values,
d = 0.93 * 0.69
d = 0.6417 meters,
The total distance covered by the needle is equal to the circumference of the record, so,
d = 2[tex]\pi \\[/tex]r
r = 0.6417/ 2*3.14
r = 0.102 meters
Therefore, the radius at which the needle is in contact moving with a velocity of 0.93 m/s and time taken 0.69 seconds is 0.102 meters.
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The complete Que is
It takes a time t = 0.69 s for a record to revolve on a record player once. A particular point on the record moves past the needle at a speed of vn = 0.93 m/s. What is the radius at which the needle is in contact with the record?
what SI units are combined to describe energy
Answer:
SI unit for energy is Joules.
in base units it will be:
1 J = 1 N·m = 1 kg·m²/s²
WILL GIVE BRAINLIEST!!!! PLEASE HELP!!!!
What is the name of the organic molecule modeled below?
A - Propane
B - Propene
C - Propine
D - Propyne
Answer:
the correct objective is C
What causes a ship carrying heavy cargo to take more time to come to a stop than an identical ship carrying lighter cargo if both ships are traveling at the same speed?.
Greater momentum causes a ship carrying heavy cargo to take more time to come to a stop than an identical ship carrying lighter cargo if both ships are travelling at the same speed.
Momentum is defined as a product of the mass of a particle and it's velocity. It is vector quantity i.e. it has both magnitude and direction. If an object is moving and has mass, it has momentum. If an object is stationary, it has no momentum. So, from this we can say that the ship carrying heavy cargo take more time to come to a stop than an identical ship carrying lighter cargo.
Mathematically,
P=mv
where P= momentum
m=mass
v=velocity
It's SI unit is kg-m/s
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A football is kicked with an initial speed of 15 m/s and an angle of 30 degrees above the field. What is the range of the football is air resistance is ignored? Round your answer to the tenths place.
The range of the football is 20m if air resistance is ignored.
What is projectile motion?When a particle is hurled obliquely near the surface of the earth, it travels along a curved path while accelerating continuously in the direction of the planet's center (we assume the particle stays close to the surface of the globe).
Such a particle's motion is known as projectile motion, and its route is referred to as a projectile.
Initial speed of the football; u =15 m/s.
angle of projection;θ = 30 degrees.
Then, horizontal range of the football is;
R = u²sin2θ/g
= (15)²sin(2×30°)/10 m.
= 20 m. (approx.)
Hence, the horizontal range of the football is 20m.
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A football is kicked with an initial speed of 15 m/s and an angle of 30 degrees above the range of the football is field 39.76 m
What is speed?The speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time it is thus a scalar quantity.
Range = u²sin 2θ/g
Range = 15²sin 60/9.8
Range = 39.76 m
A football is kicked with an initial speed of 15 m/s and an angle of 30 degrees above the range of the football is field 39.76 m
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A secondary transformer has a current of 25A and a voltage of 5V. On the primary transformer, the current is 15A. Find the primary voltage.
a.Find the primary voltage
b.What is the turns ratio Np/Ns?
c.Is this a step-up or a step-down transformer?
The primary voltage of the transformer is 8.33 V where the ratio of Np/Ns is 1.667 and the transformer is a step-up transformer.
(a) Voltage of secondary transformer (V₂) = 5 V
Current of secondary transformer (I₂) = 25 A
Current of primary transformer (I₁) = 15 A
Thus, the voltage of primary transformer (V₁) =
= using transformer equation,
= V₁ × A₁ = V₂ × A₂
= V₁ × 15 = 25 × 5
= V₁ = 8.33 V
(b) The ratio of Np/Ns =
= V₁ / V₂
= 8.33 / 5
= 1.667
(c) Since,
= 8.33 ≤ 25
= V₁ ≤ V₂
= transformer is a step-up transformer.
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Howard leans back against a wall with 50 N of force. According to Newton’s Third Law of Motion, what force is being applied and in what direction?
A.) The wall applies a force of 100 N in the opposite direction.
B.) The wall applies a force of 50 N in the same direction.
C.) The wall applies a force of 50 N in the opposite direction.
D.) The wall applies a force of 100 N in the same direction.
The wall applies a force of 50 N in the opposite direction. Option C
What is the Newton third law?According to the Newton third law, action and reaction are equal and opposite. We know that when a body exerts a given magnitude of force on a surface, the surface would also a force of equal magnitude back on the surface but the force would now be acting in the opposite direction.
This force that is exerted by the recipient of the force is what we call the reaction force. We are told here that; Howard leans back against a wall with 50 N of force. We are now going to look at the magnitude and the direction of the forces.
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Answer:
The wall applies a force of 50 N in the opposite direction.
Explanation:
Ineed of help with the units
A. The SI unit of force is the newton, symbol N.
b. The SI unit for distance is the meter (m)
c. The SI unit of work is joule (J).
or Sometimes, newton-metre (N-m) is also used for measuring work.
A rock on the edge of a cliff has a 1500 J of potential energy. The rock falls 20 m to
the ground. What is the mass of the rock? What force will be exerted on the ground on
impact?
Answer:
Mass = 7.65kg
Force = 75N
Explanation:
Energy Potential = mass • gravity • height
1500 J = mass • 9.8 • 20
1500 J/(9.8 m/s/s •20 m) = mass
7.65 kg = mass
Force = mass • acceleration
Force = 7.65 • 9.8m/s/s
Force = 75 N
We could also do 1500J/20m as gravity is divided in one and then multiplied again
Force = (1500J • 9.8m/s/s)/(9.8m/s/s • 20m)
Force = 1500J/20m
Force = 75N
this makes sense as Energy is defined as Newton metres as seen by the work formula, Work = Force • distance
Answer: Mass of the rock= 7.65g
Force exerted on the ground = 74.9N
Explanation:
potential energy = mass × gravity ×height
1500J = y × 9.8 × 20
1500J=196y
1500 ÷ 196 = y
y= 7.65g
force= mass × gravity
= 7.65 ×9.8
=74.9N
which SI units of measure describle acceleration
The meter per seconds per second (m/s²) is the SI unit of measurement used to describe an acceleration unit.
What is a acceleration explain?A rate at which position and velocity of velocity change over time is referred to as acceleration. When anything starts moving faster or slower, it's referred to as accelerating. The rate at which an object's velocity with regard to time changes is referred to as acceleration in mechanics. They are vector quantities, accelerations. The direction of a net force on the object determines the direction of its acceleration.
How do you calculate acceleration?Acceleration refers to the rate at which velocity changes over a predetermined amount of time. By divide a change in velocity even by change in time, acceleration is calculated. The acceleration of the object is equal to the net force exerted on it divided only by mass, or a = F m, in accordance with Newton's second rule of motion. When the mass of an item as well as the net force acting on are known, the acceleration of that object can be determined using this equation for acceleration.
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a hemisphere of ice with radius r rests so with its flat surface fixed to the ground. a block starts at rest at the top of the hemisphere and is given a nudge so that it slides (without friction) down the slope. how high above the ground will the block be when it looses contact with the ice (hint: what has to be zero when the block loses contact with the ice)?
The height of the block from ground is when block loses contact with the ice. This can be solved by using energy conservation and centrifugal force.
Initially the block is placed at a height of r because the height of the hemisphere would be the radius.
So total energy would be = mgr
when it is going to leave the surface, there will be some kinetic and static energy,
so total energy = 1/2 x m x v^2 + m x g x rcosФ
from conservation of energy theorem, we can write
Total energy before = total energy after
mgr = 1/2 x m x v^2 + m x g x rcosФ
2 gr = v^2 + 2 x g x rcosФ
Again, when the object is loosing the contact, that time the centrifugal force will be equal to the vertical force,
(m x v^2)/r = mgcosФ
=> v^2 = grcosФ
putting the values in the above equation
2gr = grcosФ + 2grcosФ
cosФ = 2/3
Also, we can find that when object is losing the contact, the height of the object would be = rcosФ
= r x 2/3
= 2r/3
Hence the height of the object when it is losing the contact is 2r/3.
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Suppose the energy required to freeze of water were added to the same mass of water at an initial temperature of. What would be the final temperature of the water?.
The water's final temperature under the current circumstances is 2°C.
What is the water's final temperature once the ice has melted?When a solid turns into a liquid, that temperature is known as the melting point. 32°F (0°C) is the temperature at which ice, a solid, melts into water, a liquid.
The details provided are:
Water's mass is equal to 0.25 kg.
Water's initial temperature is 1°C.
Use the following formula to calculate the water's final temperature using the law of conservation of energy:
[tex]Q_{cold}[/tex] = [tex]Q_{warm}[/tex]
mc ([tex]t_{i} -t_{f}[/tex]) = mc ([tex]t_{f} - t_{i}[/tex])
mc (1-0) = mc ([tex]t_{f}[/tex] -1)
[tex]t_{f}[/tex] = 1+1
[tex]t_{f}[/tex] = 2°C.
As a result, the water's final temperature under the current circumstances is 2°C.
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Complete question is "Suppose the energy required to freeze 0.250 kg of water were added to the same mass of water at an initial temperature of 1.0 °C. What would be the final temperature of the water?".
A dump truck, a sports car, and a bicycle are traveling at the same velocity. Which is true?.
If the dump truck, the sports car and the bicycle are travelling at the same speed then option A is true which says, the bicycle has the least kinetic energy.
We can assume here that the mass M₁ of the dump truck will be the highest and mass M₃ of the bicycle will be the lowest and the mass M₂ of the sports car will be between the mass of the dump truck and the bicycle.
So, the masses are in the order,
M₁>M₂>M₃
The dump truck the sports car and the bicycle all are moving at the same velocity V,
The kinetic energy of an object moving with velocity V and having mass M is given by,
K = 1/2MV²
So the kinetic energy of all three vehicles will be in the order,
1/2M₁V²>1/2M₂V²>1/2M₃V²
So, as per the above order the bicycle has the least kinetic energy so option A is the correct answer.
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Complete question - A dump truck, a sports car, and a bicycle are traveling at the same velocity. Which is true?
A The bicycle has the least kinetic energy.
B More information is needed to compare their kinetic energy.
C They all have the same kinetic energy.
D The sports car has the most kinetic energy.
A 50.0 kg lead block initially at 15 °C is released from rest at the top of an inclined plane with a 10° angle above the horizontal. The inclined plane is 5.00 m long. The block reaches the bottom of the inclined with a speed of 2.20 m/s. How much work is done the friction force on the block? What is the change of temperature of the block? Assume that work done by the friction force equals by magnitude the amount of heat going into the block. CL = 130 J/kg °C
Given data:
* The mass of the lead is m = 50 kg.
* The angle of the inclined plane with the horizontal is,
[tex]\theta=10^{\circ}[/tex]* The length of the inclined plane is L = 5 m.
* The speed of the lead at the bottom of the plane is v = 2.2 m/s.
* The initial temperature of the lead is,
[tex]T_i=15^{\circ}\text{ C}[/tex]* The specific heat of lead is,
[tex]c_L=130J/kg^{\circ}C[/tex]Solution:
(a). The kinetic energy of the lead at the bottom of the inclined plane is,
[tex]\begin{gathered} K=\frac{1}{2}mv^2 \\ K=\frac{1}{2}\times50\times2.2^2 \\ K=121\text{ J} \end{gathered}[/tex]The diagrammatic representation of the given case is,
From the diagram, the initial height of the block is,
[tex]\begin{gathered} \sin (\theta)=\frac{h}{L} \\ h=L\sin (\theta) \end{gathered}[/tex]Substituting the known values,
[tex]\begin{gathered} h=5\times\sin (10^{\circ}) \\ h=0.87\text{ m} \end{gathered}[/tex]The potential energy at the top of the inclined plane is,
[tex]U=\text{mgh}[/tex]where g is the acceleration due to gravity,
Substituting the known values,
[tex]\begin{gathered} U=50\times9.8\times0.87 \\ U=426.3\text{ J} \end{gathered}[/tex]The lead block is initially at rest at the top of the inclined plane, thus, the kinetic energy at the top of the inclined plane is zero.
The net energy at the top of the inclined plane is,
[tex]\begin{gathered} E_i=U+K_i \\ E_i=U+0 \\ E_i=426.3\text{ J} \end{gathered}[/tex]The height of the lead block at the bottom of the inclined plane is zero, thus, the potential energy at the bottom of the inclined plane is zero.
The net energy at the bottom of the inclined plane is,
[tex]\begin{gathered} E_f=U_f+K \\ E_f=0+121 \\ E_f=121\text{ J} \end{gathered}[/tex]Thus, the energy loss due to the friction is,
[tex]\begin{gathered} E_f-E_i=121-426.3 \\ E=-305.3\text{ J} \end{gathered}[/tex]Here, the negative sign indicates the loss of energy,
The work done by the frictional force is equal to the amount of energy loss during the motion of the lead block down the inclined plane.
Thus, the work done by the friction force on the lead is 305.3 J.
(b). The energy loss takes place in the form of heat.
The amount of heat produced in terms of the mass, temperature, and specific heat is,
[tex]Q=mc_L(T_f-T_i)[/tex]where Q is the amount of heat produced, T_f is the final temperature and T_i is the initial temperature,
Substituting the known values,
[tex]\begin{gathered} 305.3=50\times130\times(T_f-15) \\ 305.3=6500T_f-97500 \\ 6500T_f=305.3+97500 \\ 6500T_f=97805.3 \end{gathered}[/tex]By simplifying,
[tex]\begin{gathered} T_f=\frac{97805.3}{6500} \\ T_f=15.05^{\circ}\text{C} \end{gathered}[/tex]Thus, the final temperature of the lead block is 15.05 degrees celsius.