Disturbed by speeding cars outside his workplace, Nobel laureate Arthur Holly Compton designed a speed bump (called the "Holly hump") and had it installed. Suppose a 1800-kg car passes over a hump in a roadway that follows the arc of a circle of radius 21.4 m as in the figure below.(a) If the car travels at 26.6 km/h what force does the road exert on the car as the car passes the highest point of the hump?(b) What is the maximum speed the car can have without losing contact with the road as it passes this highest point?
Answers
ANSWER
[tex]\begin{gathered} (a)13,046N \\ (b)14.5m\/s\text{ or }52.2km\/h \end{gathered}[/tex]EXPLANATION
Parameters given:
Mass of the car, m = 1800 kg
Radius of arc, r = 21.4 m
(a) First, let us make a free body sketch of the problem:
where N = force exerted by the road on the car
W = weight of the car
v = velocity of the car
First, let us convert the given velocity to meters per second:
[tex]\begin{gathered} v=26.6\cdot\frac{1000}{3600} \\ v=7.39m\/s \end{gathered}[/tex]The centripetal force acting on the car as it moves in the semi-circular arc is given by:
[tex]F=\frac{mv^2}{r}[/tex]The total forces acting on the car is:
[tex]N-W+F=0[/tex]This implies that:
[tex]\begin{gathered} N=W-F \\ N=mg-\frac{mv^2}{r} \\ N=(1800\cdot9.8)-\frac{1800\cdot7.39^2}{21.4}=17,640-4,593.54 \\ N=13,046N \end{gathered}[/tex]That is the force that the road exerts on the car.
(b) At the maximum speed, the car will start to lose contact with the road at N = 0:
[tex]\begin{gathered} \Rightarrow0=W-F \\ 0=mg-\frac{mv^2_m}{r} \\ \Rightarrow\frac{mv^2_m}{r}=mg \\ \Rightarrow v^2_m=gr \\ \Rightarrow v_m=\sqrt[]{gr} \end{gathered}[/tex]Substitute the values of g and r to solve for maximum speed, vm:
[tex]\begin{gathered} v_m=\sqrt[]{9.80\cdot21.4} \\ v_m=\sqrt[]{209.72} \\ v_m=14.5m\/s \end{gathered}[/tex]In km/h, that is:
[tex]\begin{gathered} 14.5\cdot\frac{3600}{1000} \\ 52.2km\/h \end{gathered}[/tex]That is the maximum speed that the car can have.
Related Questions
Two friends challenge each other to a race up a flight of stairs (h=4.0m) Joe, who has a mass of 150kg, makes the climb in 8.0s while mike, 120kg took 5.0s to make the climb. Use g=10m/s^2
A.) Explain why joe did more work than mike.
B.) Explain why mike was more powerful than joe.
PLEASE HELP!!!
Answers
Answer:A
Explanation: i think
When work is done by a force on an object, then which of the following are true?
O The mass of the object always increases.
O The object does negative work on the force.
O The speed of the object always increases.
O The work done will be equal to the change of the total energy of the object plus energy appearing as heat, light,
O The energy lost to friction is equal to the amount of work done by the force.
Answers
Lisa is solving a vector problem, and the answer she arrives at is “17.4 m/s at 11°.” Why is this answer, as it is currently written, not complete?
Answers
This answer which is currently written is not complete because solving a vector problem, we should also mention the direction correctly, but here the direction is not mentioned.
A vector is a quantity or phenomenon that has two impartial houses, value and course. The term also denotes the mathematical or geometrical illustration of the sort of quantity. Examples of vectors in nature are pace, momentum, pressure, electromagnetic fields, and weight. A vector may be located in a square coordinate device, as illustrated here. The square coordinate notation for this vector.
vector, in physics, is a quantity that has each importance and course. it's far usually represented via an arrow whose direction is similar to that of the amount and whose period is proportional to the quantity's magnitude. although a vector has magnitude and direction, it does not have a function.
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Find the charge Q that requires 96J of energy to be moved through a potential difference of 16V ?
Answers
According to the given statement the charge Q is 6 coulomb that requires of energy to be moved through a potential difference .
What is an example of a potential difference?Note that whenever a voltage is stated, it refers to the difference in potential between two places. Every battery, for instance, has two terminals, and its voltage seems to be the difference in potential between them.
How is potential difference measured?The voltmeter is a tool used to measure potential difference. Some varieties, like voltmeters, feature a pointer on a dial, but digital displays are more common. To detect the potential difference across a circuit element, you must connect a voltmeter in parallel, unlike an ammeter.
Briefing:W is work done
V is potential difference
Work done
W = 96J
V = 16
W=Q×V
Q=W÷V
Q = 96 ÷ 16
Q = 6 Coulomb.
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A lump of lead with mass 0.50 kg is dropped from a height of 20 m onto a hard surface. It does not rebound but remains there at rest for a long period of time.
what are:
a)∆Q,(b)∆W and (c)∆U for the lead during this process?
d) What is the temperature change in the lead immediately aer the impact? [specific heat capacity of lead = 128 kJ/kg K]
Answers
The temperature change in the lead immediately ∆T=1.56 K.
Temperature is a physical amount that expresses the hotness of a count number or radiation. There are 3 sorts of the temperature scale.
Temperature is a measure of the common kinetic power of the particles in an item. when the temperature will increase, the motion of the debris also increases. Temperature is measured with a thermometer or a calorimeter.
Temperature is a degree of the common kinetic strength of the particles of a substance. The higher the temperature of an item, the better its kinetic strength. Kinetic electricity is a form of electricity related to movement.
a. ΔQ=mgh
ΔQ=0.5×9.80×20
ΔQ=98 J.
⇒∆U= ∆Q
⇒∆W=0
d. The temperature change is ∆T=1.56 K
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The Hubble Space Telescope has a resolution of about 0.05″. What is the size of the smallest feature it can distinguish on the surface of Mercury, at closest approach to Earth?
Answers
If the Hubble Space Telescope has a resolution of about 0.05, then the size of the smallest feature it can distinguish on the surface of Mercury, at closest approach to Earth is 92 m.
What is the earth?
The Earth is described as an ellipsoid with a circumference of about 40,000 km. The earth found is the densest planet in the Solar System and it is also the largest of the four rocky planets.
The Hubble Space Telescope is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. It was not the first space telescope, but it is one of the largest and most versatile, renowned both as a vital research tool and as a public relations boon for astronomy.
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Help!! Vector V is 448 m long in a 224 direction. vector W is 336 m long in a 75.9 direction. Find the direction of their vector sum.
Answers
The Direction of the vector sum of the two vectors V and W is resulted as 240.84 m toward + x.
What is a vector?A vector is a quantity or phenomenon with independent components of magnitude and direction. The expression can also be used to describe a quantity's geometric or mathematical representation.
The following are the x and y axes for the supplied vector:
Vector V in x direction;
[tex]$$\begin{aligned}&\mathrm{V}_{\mathrm{x}}=\mathrm{V} \cos \theta \\&\mathrm{V}_{\mathrm{x}}=448 \cos \left(224^0\right) \\&\mathrm{Vx}=-322.26\end{aligned}[/tex]
Vector V in y direction;
[tex]\begin{aligned}&V_y=V \sin \theta \\&V_y=448 \times \sin 224^0 \\&V_y=-311.2\end{aligned}[/tex]
Vector W in x direction;
[tex]W_x = 336 \times cos(74.9^0)[/tex]
[tex]W_x = 81.86[/tex]
Vector W in y direction;
[tex]\begin{aligned}&\mathrm{W}_{\mathrm{y}}=336 \times \sin 75.9 \\&\mathrm{W}_{\mathrm{y}}=325.88\end{aligned}[/tex]
The resultant vector in the x direction is;
[tex]\begin{aligned}&\Sigma X=-322.26+81.86 \\&\Sigma X==-240.4\end{aligned}[/tex]
The resultant vector in the y direction is;
[tex]\begin{aligned}&\Sigma Y=-311.2+325.88 \\&\Sigma Y=14.68\end{aligned}[/tex]
The resultant vector is found as;
[tex]\begin{aligned}&\mathrm{R}=\sqrt{(-240.4)^2+(14.68)^2} \\&\mathrm{R}=240.84 \mathrm{~m}\end{aligned}[/tex]
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Compute the average acceleration during the time interval t=0 to t=10s .
Express your answer in meters per second squared to two significant figures
Answers
The average acceleration during the time interval t=0 to t=10s is 1.67 m/s².
What is average acceleration?
The average acceleration of an object is the rate of change of velocity of an object with time.
Mathematically, the average acceleration of an object is given as;
a = Δv/Δt
a = (v₂ - v₁)/(t₂ - t₁)
where;
v₂ is the final velocityv₁ is the initial velocityt₂ is the final time of motiont₁ is the initial time of motionFrom the graph,
the initial velocity at time of 0 second = 0 km/h
the final velocity at time of 10 seconds = 60 km/h = 16.67 m/s
the initial time = 0 s
the final time = 10 s
The average acceleration of the car is calculated as follows;
a = (16.67 m/s - 0 m/s) / (10 s - 0 s)
a = 1.67 m/s²
Thus, the average acceleration of the car increases with increase in the rate of change of displacement with time.
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Cindy runs 2 km every morning. She takes 2 minutes for the first 250 m, 4 minutes for the next 1,000 m, 1 min for the next 350 m, and 3 min for the rest.
Cindy's average speed for the entire run is ______ m per min. One km is the same as 1,000 m.
Hint: average speed = total distance/total time
Answers
Cindy's average speed for the entire run is 200 m per min.
What is Cindy's average speed for the entire run?
First, to measure Cindy's average speed, we need to know that the average speed of Cindy would be the total distance she had covered while running by the total amount of time it took her to cover the distance. So, we need to measure her average rate of speed over the extent of her runs.
In order to calculate average speed we will calculate the total distance in meters traveled by Cindy.
Given:
Total distance = 2 Km
Convert km to meter, since she is running at a different speed measured in meter.
1 km = 1,000 m
Total distance = 2 Km = 2000 m
Then, the total amount of time in minutes it took her to cover this distance is: 2 (for the first 250 m) + 4 (for the next 1,000 m) + 1 (next 350 m) + 3 (time used for rest) = 10 minutes
Average speed = total distance / total time
Average speed = 2000 m / 10 minutes
Therefore, her average speed = 200 m per min
In summary, Cindy, though rested for 3 minutes, maintained an average speed of about 200 m per min for the entire run.
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Which has the greatest mass between a Volleyball,Basketball and Soccer ball?
Answers
A student is investigating the specific heat capacity of a block of iron. Their method is to heat up the insulated block of iron using an electric heater and measure its temperature using a digital thermometer at regular intervals. The block will be heated up from room temperature to 80
°C. What is the independent variable in this experiment?
• The increase in temperature of the block of iron
• The mass of the block of iron
The time the block of iron takes to reach 80 °C
The energy supplied to the block of iron by the electric heater
Answers
As we carry out the experiment, the independent variable here is the he increase in temperature of the block of iron.
What is an experiment?In many instances, it is very important for us to be able to understand the cause and effect relationship that is likely to exists between two variables. The only way that we could be able to in fact deduce the cause and effect relationship that does exist when we have two variables is by the use of an experiment.
Hence, when ever we are doing an experiment there must be an independent variable as well as well as a dependent variable. The variable that we are manipulating in the experiment is the independent variable. The dependent variable changes as we manipulate the independent variable.
As such, in the case of this experiment, the independent variable here is the increase in temperature of the block of iron.
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12. Which of the following is not a property
of metals?
13. Which of the following correctly lists
the elements in order of increasing size
(smallest to largest)?
[orange]
conduct electricity
[yellow]
Sr
[blue]
[red]
brittle
[green]
Ca
[black]
[yellow]
shiny
[purple]
Be
[purple]
Answers
Be [purple], Ca [black] and Sr [blue] are the elements in order of increasing size.
Brittle is not the property of metals.
Why brittle is not the property of metals?The strong electrostatic force of attraction that is present in metal ions when they are surrounded by a large number of electrons. It is actually very strong and flexible at the same time. So, when we apply a force on the metals, they can be transformed into flat and smooth sheets that can be drawn into wires and they are hard to break into pieces.
Beryllium is an element that is present in the second period while on the other hand, calcium element is present in the next period and Sr element is also present in the lower period of periodic table. We know that when we move down the group, the number of shells increases which ultimately leads to increase in atomic size.
So we can conclude that the elements in order of increasing size are Be [purple], Ca [black] and Sr [blue]. The property which is not present in metals is the property of metals.
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Please help!⚠️ Find the direction of this vector: -22.2 m, 12.6 m
Answers
Answer: The direction of the resultant can be determined by finding the angle that the resultant makes with either the north-south or the east-west vector. The diagram at the right shows the angle theta (Θ) marked inside the vector addition triangle. This angle theta is the angle that the resultant makes with west.
Explanation: Hope this helps.
Answer:
Magnitude=25.5
Direction=-60.4
Explanation:
[tex]\sqr\sqrt{ x^{2} +y^{2} \\\\[/tex]=m
[tex]Tan^{-1} (y/x)[/tex] = D
Which is the following is an example of oxidation reaction??
Answer: Rusting
rust is an oxidation reaction only when iron reacts with water and oxygen.
Answers
Rusting is referred to as a example of oxidation reaction in this type of context.
What is Oxidation?This is a type of chemical change which involves the loss of electrons and contact with oxygen molecules. When this occurs, the element becomes oxidized with the symbol O which is being used to denote it. The main factor which is considered about the oxidation process is the availability of oxygen.
Rusting on the other hand is referred to as iron oxide which occurs during the reaction between iron and oxygen and the color changes into reddish brown which signifies this process.
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(PLEASE ANSWER) Which of the following conditions would result in the greatest amount of gravitational force between a planet and it's moon? Select THREE answers.
A. The mass of the planet is small.
B. The mass of the moon is small.
C. The distance separating the planet and moon is small.
D. The mass of the planet is large.
E. The mass of the moon is large.
F. The distance separating the planet and moon is large.
Answers
Answer:
[tex] \small \fbox{\sf Option C, D and E are the correct answer.}[/tex]
Explanation:
The gravitational force of attraction between any two masses is given by the formula,
[tex]F = G \frac{m_1 \cdot m_2}{r^2}[/tex]
Where,
F is force of attraction between masses,m1 is mass of object 1 say planet, m2 is mass of object 2 say moon,r is the distance separating the planet and moon.From above relation we can conclude that,
Gravitational force of attraction is directly proportional to the product of masses of each object.Gravitational force of attraction is inversely proportional to the distance separating the planet and moon.Hence, the greatest amount of gravitational force between a planet and it's moon would be largest when,
The mass of the planet is large.The mass of the moon is large.The distance separating the planet and moon is small.Option C, D and E are the correct answer.
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When someone throws a ball, the action force is the person pushing on the ball. What is the reaction force?
the ball pushing on the person
the ball pushing against air
the ball being pulled toward the ground
the ball being pulled away from the person
Answers
Answer:
the ball being pulled toward the ground
Explanation:
An electrical vacuum tube was sealed off during manufacturing at a pressure of 1.2 *10^7 mmhg at 27degree Celsius and volume of 100cm what is the pressure of the tube and how mana gas of molecule remain in the tube
Answers
3.86×10^11 molecules of gas remain in the tube
P = nkT
n = P/kT
= hdg/kT
Number of molecules in the electron tube is = n×V = hdgV/kT
⟹n = hdg/kT
=
1.2×10^−10 ×13600 × 9.8 × 100 × 10^−6/1.38×10^−23 × 300
= 3.86×10^11
Is it safe to stay inside a vehicle during a heavy storm?
Answers
Answer:
Like trees, houses, and people, anything outside is at risk of being struck by lightning when thunderstorms are in the area, including cars. The good news though is that the outer metal shell of hard-topped metal vehicles does provide protection to those inside a vehicle with the windows closed.
Answer: Depends
Explanation:
You should be good if you have proper shelter and protection to maintain safety.
If it's hail, it's probably best to find shelter and I recommend putting a thick blanket on the windows so they don't burst.
Which trial has the greatest impulse?
trial 1
trial 2
trial 3
trial 4
Answers
difference between weight and mass.
please be honest. don't answer if you don't know
Answers
Weight is the gravitational force with which the earth pulls an object towards it whereas, Mass is a quantity representing the amount of matter in a particle or object.
hope this helps and you need a chair for sitting xD -,-
a 5.5 kg box is pushed across the lunch table. The net force applied to the box is 9.7N. what is the acceleration of the box.
Answers
Answer:
1.8 m / s^2
Explanation:
F = ma ( ignoring friction)
F/ m = a
9.7 / 5.5 = 1.8 m/s^2
the bus stops at distance of 25 metres, calculate the force that was needed to stop the bus in N
Answers
The force that was needed to stop the bus of mass 5000 kg that stops after 25 m in 5 s is 5000 N.
a = v / t
v = d / t
a = Acceleration
v = Velocity
d = Distance
t = Time
d = 25 m
t = 5 s
v = 25 / 5
v = 5 m / s
a = 5 / 5
a = 1 m / s²
According to Newton's second law of motion,
F = m a
F = Force
m = Mass
m = 5000 kg
F = 5000 * 1
F = 5000 N
The given question is incomplete. The complete question is:
A bus of mass 5000 kg applies brake and stops after 5 seconds and the bus stops at distance of 25 meters, calculate the force that was needed to stop the bus in N
Therefore, the force that was needed to stop the bus is 5000 N
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TRUE or FALSE: The Equator receives less solar energy than other latitudes.
Answers
Answer: False
Explanation: the equator receives the most sun light because the the equator is closest to the sun.
A motorcyclist is traveling in the positive direction at a
velocity of 7.0 meters per second. She increases her
velocity to 9.0 meters per second. What additional
information is needed to calculate the acceleration of
the motorcycle?
Answers
The additional information needed to calculate the acceleration of the motorcycle is the time taken to complete the distance.
What is acceleration?Acceleration is the amount by which a speed or velocity increases (and so a scalar quantity or a vector quantity).
The acceleration of a moving body can be calculated by dividing the change in velocity of the motion (∆V) by the time taken to complete the motion as follows:
Acceleration (m/s²) = change in velocity (m/s)/time(s)
According to this question, a motorcyclist is traveling in the positive direction at a velocity of 7.0 meters per second. She then increases her velocity to 9.0 meters per second. This means that the change in velocity {∆V} is 2m/s.
However, the time taken to complete the distance is still required to compute the acceleration of the motorcycle.
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A rabbit is moving in the positive x-direction at 1.50 m/s when it spots a predator and accelerates to a velocity of 12.1 m/s along the positive y-axis, all in 2.20 s. Determine the x-component and the y-component of the rabbit's acceleration. (Enter your answers in m/s2. Indicate the direction with the signs of your answers.)
Answers
Acceleration of the rabbit, moving in the positive x-direction at 1.50 m/s when it spots a predator and accelerates to a velocity of 12.1 m/s along the positive y-axis, all in 2.20 s is given by in x direction 0 m/sec² in y direction is 5.50 m/sec².
What is acceleration?The rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting.
Given in the question rabbit is initially moving with speed 1.50 m/sec in x direction after rabbit spot predator start accelerating in y direction to velocity 12.1 m/sec in 2.20 m. so acceleration in x direction will be zero.
Acceleration in y direction is 5.50 m/sec².
Acceleration in x direction will be zero.
Acceleration in y direction is 5.50 m/sec².
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An impulse of 24 Ns acts on a baseball from a bat. What is the force applied to the ball from bat if the ball is in contact with the ball for only 0.0007s.
Answers
The force applied to the ball from bat if the ball is in contact with the ball for only 0.0007 s is 34.29 KN
J = F * t
J = Impulse
F = Force
t = Time
J = 24 N s
t = 0.0007 s
F = J / t
F = 24 / 0.0007
F = 34.29 KN
Impulse is the rate of change of momentum in an object. It can simply be defined as force acting on an object over a period of time to change the object's momentum. So,
J = Δp = F Δt
Therefore, the force applied to the ball from bat is 34.29 KN
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While scuba diving, Alec is rising toward the surface of the water at 6.0 meters per minute. If his velocity remains constant, how much time will it take Alec to rise 8.4 meters?
Answers
Given data
*Alec is rising towards the surface of the water is u = 6.0 m/min
*The given distance is d = 8.4 m
The formula for the time taken by the Alec to rise is given as
[tex]t=\frac{d}{u}[/tex]Substitute the values in the above expression as
[tex]\begin{gathered} t=\frac{8.4}{6.0} \\ =1.4\text{ minute} \end{gathered}[/tex]Hence, the time is taken by Alec to rise is t = 1.4 minutes
Give 5 example of a factual statement and five example of an opinion
Answers
Three point charges -Q, -Q, and +3Q are arranged along a line as shown in the sketch.
What is the electric potential at the point P?
A) +kQ/R
B) -2kQ/R
C) -1.6kQ/R
D) +1.6kQ/R
E) +4.4kQ/R
Answers
(D) The electric potential at the point P is +1.6 kQ/R.
What is electric potential?
The electric potential of a given charged body is the work done in bringing the charge from a point to a given location in the electric field.
Mathematically, electric potential is given as;
V = kq/r
where;
k is Coulomb's constantq is magnitude of the charger is radius of the chargeThe distance of each of the negative charge to point P is calculated as follows;
r = √(R² + R²)
r = √(2R²)
r = R√2
The electric potential from each negative charge to point P;
V = -kQ/(R√2)
For the two charges = - 2kQ/(R√2)
The electric potential from 3Q
V = (k3Q) / R
V = (3kQ)/R
The total electric potential;
V(net) = (3kQ)/R - 2kQ/(R√2)
V(net) = (3kQ)/R - (1.414kQ)/R
V(net) = +1.6 kQ/R
Thus, we can conclude that the sum of the sum of the electric potential at point must be positive since it is directed to the positive y-direction.
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A pipe of length 10.0 m increases in length by 1.5 cm when its temperature is increased by 90°F. What is its coefficient of linear expansion?
Answers
The coefficient of linear expansion, given that the length of the pipe increased by 1.5 cm is 1.67×10¯⁵ /°F
How to determine the coefficient of linear expansionFrom the question given above, the following data were obtained
Original diameter (L₁) = 10 mChange in length (∆L) = 1.5 cm = 1.5 / 100 = 0.015 mChange in temperature (∆T) = 90 °FCoefficient of linear expansion (α) =?The coefficient of linear expansion can be obtained as illustrated below:
α = ∆L / L₁∆T
α = 0.015 / (10 × 90)
α = 0.015 / 900
α = 1.67×10¯⁵ /°F
Thus, we can conclude that the coefficient of linear expansion is 1.67×10¯⁵ /°F
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