A car rounds a banked curve as we will discuss in class on Tuesday. The radius of curvature of the road is R and the banking angle is θ. (a) In the absence of friction, what is the safe speed for the car to take this curve? (b) Now assume the coefficient of friction between the car’s tires and the road is µs. Determine the range of speeds the car can have without slipping up or down the road. (c) What is the minimum value of µs that makes the minimum speed zero? (d) If θ = 25.0 ◦ , for what values of µs can the curve be taken at any speed? Note: The upper limit of µs you will find is practically impossible to achieve for the car’s tires and the road.

Answers

Answer 1

Answer:

A) v = √[(rg(tan θ - µ_s))/(1 + (µ_s•tan θ))]

B)√[(rg(tan θ - µ_s))/(1 + (µ_s•tan θ))] ≤ v ≤ v = √[(rg(tan θ + µ_s))/(1 - (µ_s•tan θ))]

C) µ_s = tan θ

D) µ_s = 0.4663

Explanation:

A) The forces acting on the car will be;

Force due to friction; F_f

Force due to Gravity; F_g

Normal Force; F_n

Now, let us take the vertical direction to be j^ and the direction approaching the centre to be i^ downwards and parallel to the road surface by k^.

Also, we will assume that initially, F_n is in the negative k^ direction and that it will have a maximum possible value of; F_f = µ_s × F_n

Thus, sum of forces about the vertical j^ direction gives;

ΣF_j^ = F_n•cos θ − mg + F_f•sin θ = 0

Since F_f = µ_s × F_n ;

F_n•cos θ − mg + (µ_s × F_n × sin θ) =0

F_n = mg/[cos θ + (µ_s•sin θ)]

Also, sum of forces about the centre i^ direction gives;

ΣF_i^ = F_n(sin θ + (µ_s•cos θ)) = mv²/r

Plugging in formula for F_n gives;

ΣF_i^ = [mg/[cos θ + (µ_s•sin θ)]] × (sin θ + (µ_s•cos θ)) = mv²/r

Making v the subject gives;

v = √[(rg(tan θ - µ_s))/(1 + (µ_s•tan θ))]

B) What we got in a above is the minimum speed the car can have while going round the turn.

The maximum speed will be gotten by making the frictional force(F_f) to point in the positive k^ direction. This means that F_f will be negative.

Now, if we change the sign in front of F_f in the equation in part a that led to the minimum velocity, we will have the maximum as;

v = √[(rg(tan θ + µ_s))/(1 - (µ_s•tan θ))]

Thus the range is;

√[(rg(tan θ - µ_s))/(1 + (µ_s•tan θ))] ≤ v ≤ v = √[(rg(tan θ + µ_s))/(1 - (µ_s•tan θ))]

C) For the minimum speed to be 0, it implies that F_f will be in the negative k^ direction. Thus, Sum of the forces in the k^ direction gives;

ΣF_k^ = mg(sin θ - µ_s•cos θ) = 0

Thus;

mg(sin θ - µ_s•cos θ) = 0

Making µ_s the subject gives;

µ_s = sin θ/cos θ

µ_s = tan θ

D) If θ = 25.0°;

Thus;

µ_s = tan 25

µ_s = 0.4663


Related Questions

David drove the first 6 hours of his journey at 65km/hr and the last 3 hours of his journey at 80km/hour. How far is the whole journey in km?

Answers

630 kilometers for the whole journey

The neutrons in the nucleus of an atom have-
a. a positive charge
b. a negative charge
C. both positive & negative charges
d. no charge

Answers

Answer "d' no charge

Explanation:

They are as the name says neutral. They have no charge they are electrically neutral. Just as a proton is a positively charged particle and an electron carries a negative charge.

The neutrons in the nucleus of an atom have:
D. No charge

PLEASE PROVIDE EXPLANATION FOR D AND E

THANK YOU!

Answers

Answer:

d) 14.1 m

e) 8.57 m/s

Explanation:

(a) There are three forces on the ball:

Normal force Fn pushing up,

Weight force Fg pulling down,

Kinetic friction Fk pushing left (resisting motion).

FBD is the correct free body diagram.

(b) Sum of forces in the y direction:

∑F = ma

Fn − Fg = 0

Fn = Fg

Sum of forces in the x direction:

∑F = ma

-Fk = ma

-Fn μk = ma

-mg μk = ma

a = -g μk

a = -(10 m/s²) (0.25)

a = -2.5 m/s²

(c) Sum of torques about the ball's center:

∑τ = Iα

Fk r = ⅖ mr² α

mg μk r = ⅖ mr² α

g μk = ⅖ r α

α = 5g μk / (2r)

α = 5 (10 m/s²) (0.25) / (2 × 0.2 m)

α = 31.25 rad/s²

(d) The velocity and angular velocity at time t is:

v = at + v₀

v = -2.5t + 12.0

ω = αt + ω₀

ω = 31.25t + 0

When the ball begins to roll without slipping, v = ωr.

-2.5t + 12.0 = (31.25t) (0.2)

-2.5t + 12.0 = 6.25t

12.0 = 8.75t

t = 1.37

The distance the ball moves is:

Δx = v₀ t + ½ at²

Δx = (12) (1.37) + ½ (-2.5) (1.37)²

Δx = 14.1 m

(e) v = at + v₀

v = (-2.5 m/s²) (1.37 s) + 12.0 m/s

v = 8.57 m/s

Answer:

a

Explanation:

on egde 2020

Which of the following is true as a ball that was thrown straight up into the air is traveling up?
A. The acceleration is upward until it stops and the acceleration becomes downward. The object is also slowing down as it rises.
B. The acceleration is downward as the object moves up. This causes the object to slow down until it stops and then speed up as it falls down.

Answers

Answer:

b

Explanation:

when a ball falls from the sky, it falls down fast due to no friction.

The answer should be B.

What type of energy transfer causes a sunburn?
A. Radiation, because particles of hot air move in space
B. Radiation, because electromagnetic waves transfer heat
C. Conduction, because hot air comes in contact with the skin
D. Conduction, because invisible light carries heat from the sun
If your right you get 100 points and a brainliest

Answers

Answer:

Hi!!

It should be A, ratation

(sorry that I didnt spell that write)

Have a great day!

To solve this we must be knowing each and every concept related to energy and its different types. Therefore,  the correct option is option A among all the given options.

What is energy?

In physics, energy is the capacity to accomplish work. It can be potential, kinetic, thermal, electric, chemical, radioactive, or in other forms.

There is also heat and work—energy inside the process of being transferred by one body to the other. Energy is always classified according to its type once it has been transmitted. As a result, heat transported could become thermal energy, whereas labor done may emerge as mechanical energy. Radiation is a t type of energy that transfer energy that causes a sunburn  because particles of hot air move in space.

Therefore,  the correct option is option A among all the given options.

To know more about energy, here:

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A force of 150. N is exerted 22° north of east. Find the northward and eastward components of this force.

PLEASE HELP ASAP

Answers

Answer: northward would be 139 N

Explanation:

Three sticks are arranged in such a way that they form a right triangle. The
lengths of the three sticks are 0.47 m, 0.62 m, and 0.78 m. What would the
three angles of this triangle? *

Answers

Answer:

one right angel = 90 degrees

and two acute angels?

Explanation:

2. What is the normal force acting a 800-kg car if there are two 55-kg people sitting inside the car?

Answers

Total mass = 800 + 55 + 55 = 910 Kg
Normal force = 910 x 9.8 = ... Newton

a spring scale is constructed so that each 0.10-n increment is separated by 0.50 cm. what spring constant is necessary for the scale to be accurate?

Answers

Answer:

5.00

Explanation:

How much work does an athlete do if she
raises a 5N kettle bell 2 m off the ground?

Answers

Answer:

The answer is 10 N

Explanation:

To find the work done by an object given the distance covered by the object and it's force we use the formula

work done = force × distance

From the question

force = 5 N

distance = 2 m

We have

work done = 5 × 2

We have the final answer as

10 N

Hope this helps you

A family is visiting the Statue of Liberty in New York City. One of the children accidentally drops her backpack from the top of the viewing platform which is 300 feet above the ground. At what height will the kinetic energy of the backpack be equal to it's potential energy?

Answers

Have you figured out this answer yet. Pls say yes

In fact the actual height at which the two energies are equal can be determined only if there is a specified velocity. So by theoretically equating the energy equation we will arrive at the point that the height equal to 4.9 V².

What is kinetic energy?

The kinetic energy of a body is the energy formed by virtue of its motion. It is directly proportional to the mass and velocity of the moving body and the equation is written as:

KE = 1/2 MV².

Potential energy is formed by virtue of the position of a body and it is equal to mgh. Where, g is gravitational acceleration equal to 9.8 m/s² and m is mass and h is the height from the ground.

The total of these two energy is called mechanical energy of a body and the total mechanical energy of a body is always conserved.

If the kinetic energy and potential energy are equal then the equations can be equated as:

1/2 mV² = mgh

 V²/2 = gh.

         =9.8 h

 h  = 4.9 V²

Therefore at a height of 4.9 V² the energies of the falling body will be equal where v is the velocity of the moving body.

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classify the planets as inner planets of outer planets explain your answer​

Answers

Answer: Planets A and B have a rocky mantle and an iron core. They are at a distance of 1 AU or less from the Sun. This means they are relatively close to the Sun. There are the properties of inner (terrestrial) planets. So planet A and B are inner planets.

Explanation:

Planet C is composed if the gases hydrogen and helium. It has a high mass and is much farther from 1 AU from the sun. These properties are consistent with the outer planets. So, planet C is an outer (gas giant) planet.

Answer:

Planets A and B have a rocky mantle and an iron core. They are at a distance of 1 AU or less from the Sun. This means they are relatively close to the Sun. There are the properties of inner (terrestrial) planets. So planet A and B are inner planets.

Explanation:

a force of magnitude 30 n stretches a spring 0.83 m from equilibrium. what is the value of the spring constant?

Answers

Answer:

36 N/m

Explanation: I got the answer right on the test ight noo cap

Activity_Mass_Balance_Recycle
Sea water must be desalinated by reverse osmosis. For a feed rate of 1000 lb/h sea water containing 3.1% salt (by weight) is desalinated water with only 500 ppm salt and the brine tailings containing 5.25% salt. Part of the brine tailings is recycled and the inlet stream in the reverse osmosis cell contains 4.0% salt. Determine:

a) A brine removal taxon (ṁ3);
b) The production rate of desalinated water (ṁ2);
c) The rate of brine that is recycled (ṁR).

Answers:

ṁ1 = 1720 lb / h

ṁ2 = 409.37 lb / h

ṁ3 = 590.63 lb / h

ṁR = 720 lb / h

Answers

Answer:

m₁ = 1720

m₂ = 413.46

m₃ = 586.54

mr = 720

Explanation:

Draw a diagram.  Sea water (1000 lb/h, 3.1% salt) is mixed with the recycled brine (mr, 5.25% salt) to create the inlet stream (m₁, 4.0% salt).  This inlet stream is fed into the osmosis cell.  The osmosis cell produces desalinated water (m₂, 500 ppm) and brine tailings.  Part of the tailings is recycled (mr, 5.25% salt), and the rest is removed (m₃, 5.25%).

The mass of water is conserved, so:

1000 + mr = m₁

m₁ = mr + m₂ + m₃

The mass of salt is conserved, so:

0.031 (1000) + 0.0525 mr = 0.040 m₁

0.040 m₁ = 0.0525 mr + 0.0005 m₂ + 0.0525 m₃

Four unknown variables, and four equations.  We can use the first and third to find mr and m₁.

0.031 (1000) + 0.0525 mr = 0.040 (1000 + mr)

31 + 0.0525 mr = 40 + 0.040 mr

0.0125 mr = 9

mr = 720

m₁ = 1720

Now we can use these values and the second and fourth equations to solve for the remaining variables.

1720 = 720 + m₂ + m₃

0.040 (1720) = 0.0525 (720) + 0.0005 m₂ + 0.0525 m₃

1000 = m₂ + m₃

68.8 = 37.8 + 0.0005 m₂ + 0.0525 m₃

68.8 = 37.8 + 0.0005 m₂ + 0.0525 (1000 − m₂)

68.8 = 37.8 + 0.0005 m₂ + 52.5 − 0.0525 m₂

0.052 m₂ = 21.5

m₂ = 413.46

m₃ = 586.54

which theory says dreaming is an unimportant by-product of neural firing during sleep

Answers

Answer:activation-synthesis

Explanation:

If a 3.5 kg object is accelerating at 0.80 /s^2, the net force F causing this motion is ____ N.

A) 2.2
B)2.8
C)3.4
D)4.0

Answers

Answer:

The answer is option B

Explanation:

To find the force acting on an object we use the formula

force = mass × acceleration

From the question

mass = 3.5 kg

acceleration = 0.80 m/s²

We have

Force = 3.5 × 0.8

We have the final answer as

2.8 N

Hope this helps you

A capacitor consists of two closely spaced metal conductors of large area, separated by a thin insulating foil. It has an electrical capacity of 3000.0 μF and is charged to a potential difference of 60.0 V. Calculate the amount of energy stored in the capacitor. Tries 0/20 Calculate the charge on this capacitor when the electrical energy stored in the capacitor is 6.53 J. Tries 0/20 If the two plates of the capacitor have their separation increased by a factor of 5 while the charge on the plates remains constant, by what factor is the energy stored in the capacitor increased?

Answers

Answer:

1 = 5.4 J

2 = 0.1979 C

3 = 5

Explanation:

Energy in a capacitor, E is

E = 1/2 * C * V²

E = 1/2 * 3000*10^-6 * 60²

E = 1/2 * 3000*10^-6 * 3600

E = 1/2 * 10.8

E = 5.4 J

E = Q²/2C = 6.53 J

E * 2C = Q²

Q² = 6.53 * 2 * 3000*10^-6

Q² = 13.06 * 3000*10^-6

Q² = 0.03918

Q = √0.03918

Q = 0.1979 C

The Capacitor, C is inversely proportional to the distance of separation, D. Thus, if D is increased by 5 to be 5D, then C would be C/5. And therefore, our energy stored in the capacitor is increased by a factor of 5.

What is the amount of thermal energy that can be stored in an object depends on?

Answers

Thermal energy is the total energy of all the molecules in an object. The thermal energy of an object depends on three things: 4 the number of molecules in the object 4 the temperature of the object (average molecular motion) 4 the arrangement of the object's molecules (states of matter).

Hope this helps

• An evacuated long tube contains a coin and a feather. If both objects fall together starting from the top of the tube, it is expected that:
(a) the coin will reach the bottom first.
(b) the feather will reach the bottom first.
(c) both objects will reach the bottom at the same instant.

• If this experiment is repeated at a place 2000 kilometers above the sea-level, the acceleration due to gravity gexp is expected to :
(a) increase. (b) decrease. (c) remain constant.

Answers

Answer:

c-) both objects will reach the bottom at the same instant.

(b) decrease.

Explanation:

Although the feather is lighter than the coin, the tube where the experiment is performed is evacuated. Therefore there is no air that prevents the feather from falling freely with the same acceleration and speed as the coin.

In fact in the equations of kinematics proposed by Newton, the mass of the bodies is not taken into account, as we can see in the following equation:

[tex]v_{f}= v_{i} +g*t[/tex]

where:

Vf = final velocity [m/s]

Vi = initial velocity [m/s]

g = gravity acceleration [m/s^2]

t = time [s]

Therefore the answer is C.

Gravitational pull is a function of height, as the height of the body increases, the force of gravity decreases.

A baseball player is running at a constant velocity on a level field and tosses a baseball straight up. When the ball comes back down, it will land

Answers

Answer:

]

Explanation:

6. What velocity vector will move you 200 miles east in 4 hours travelingat a constant speed?

Answers

Answer:

50 mph east

Explanation:

What is the speed of a car that travels 0.200 km in 95 seconds? State your answer in meters per second.

Answers

Answer:

2.10 meters per second

Explanation:

speed (velocity) = distance / time

                          = 0.2 km (1000 m/km)

                                     95 secs.

                          = 2.10 meters per second

Lexington walked to her friends house.lexie walked 2miles west then 5 miles south then 3 miles east then 4 miles north then 2 miles east and finally 1 mile north what is levies distance and displacement.​

Answers

The answer is 17 for the miles

give at least two similarities and differences among the terrestrial planets Mars Venus and Earth​

Answers

Answer:

Answer is as follow:

Explanation:

With a distance of just 6,792 km, Mars is even smaller. And again, Venus would be almost Earth's double in terms of scale. It has 81 percent of the earth 's volume, while Mars has just 10 percent of the earth 's mass. Mars and Venus have very different ecosystems, and they are both very separate from Earth.

This chart shows Dan's budget:
Did Dan stay on budget? Why or why not?
Amount budgeted
tem
nome
Food
Rent
Debonary spending
Income
$100
S500
$100
5750
Amount spent
55
S90
3500
5140
Yes, Dan spent as much as he earned.
No, Dan should move to a new apartment
O Yes, Dan uses his savings to cover extra expense
No, Dan should reduce his discretionary spending,

Answers

Answer

No dan should reduce his discretionary apendings.

Explanation:

Amass oscillates in simple harmonic motion with amplitude A , if the mas is halved , but the amplitude is not changed , what will happen to the total mechanical energy of the system​

A- It will increase
B-it will decrease
c-It will stay at the same
D-None of these

Answers

B but im not so sure, best of luck tho!!

1. A tourist accidentally drops a camera from a 40.0 m high bridge and it falls for 2.85 seconds. If g = 9.81 m/s2 and air resistance are disregarded, what is the speed of the camera as it hits the water?

Answers

Answer:

28 m/s

Explanation:

v(final)^2=v(initial)^2+2a(delta y)

=sqrt(2*-9.8 m/s^2*-40)

28 m/s

The speed of the camera with which it hits the water is 27.93 meters per second.

What is the speed?

The speed of an object is the rate of change of position of an object in any of the directions. Speed can be measured as the ratio of distance covered by the object to the total time taken in which the distance was covered by the object. Speed is a scalar quantity because it has only magnitude and no direction.

v = gt

where, v is the velocity,

g is the acceleration due to gravity,

and t is the time taken by the object

v = (9.8 m/s²) (2.85s)

v = 27.93 m/s

Therefore, the speed of the camera as it hits the water is 27.93 meters per second.

Learn more about Speed here:
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Light refracts when traveling from air into glass because light
O A Travels at the same speed in air and in glass
B Frequency is greater in air than in glass
OC Frequency is greater in glass than in air
D Travels slower in glass than in air

Answers

Answer:

the last one

Explanation:

ii took the quiz and it was right... i think

- You travel by bus from Indianapolis to New York City which is 1100 miles away. With no stops, the trip took 11 hours. The average speed was...​

Answers

Answer:

100 mph, or about 44.7 m/s

Explanation:

Average speed is [tex]\frac{distance}{time\\}[/tex].

After substitution, this is [tex]\frac{1100}{11}[/tex].

The average speed, therefore, reduces to 100 mph, or about 44.7 m/s.

A car travels 45 km due north and 70 km west. What is the car's displacement?
6 points
24.7 km northeast
83.2 km northwest
76.5 km northwest
115 km north

Answers

Answer:

A

Explanation:

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