Mary and John are seated on a bench a distance 2 part. Suddenly, John moves closer to Mary and claims that he has been drawn by the gravitational force. Is John’s claim justifiable? Show quantitatively. (Assume the masses of John and Mary are 67 and 55 respectively, and the coefficient of static friction between John and the bench is 0.15). [4]

The maximum speed at which a car could go around this curve without slipping is6.12m/s

To solve this it is necessary to take concepts related to Centripetal Force and Friction Force.

In the case of the centripetal force,

Fc = mv²/r      ....1

Where,

m=mass

v= velocity

r= Radius

In the case of the Force of Friction we have to,

F= [tex]\mu[/tex]mg      ......1.

Where,

[tex]\mu[/tex] = Friction Constant

m= mass

g= gravity

the centripetal equal to the friction force to stay on the road, in this way

mv²/r  = [tex]\mu[/tex]mg      

v² = mgr

v = √([tex]\mu[/tex]gr)

The coefficient of friction between the cars' tires and the track

 [tex]\mu[/tex] = 0.50

radius = 800m

g = 9.8 m/s²

using above values we get

v = [tex]\sqrt[]{800*9.8*0.5}[/tex]

V = 6.12m/s

The maximum speed at which a car could go around this curve without slipping is6.12m/s

To know more about coefficient of friction

https://brainly.com/question/13932862

#SPJ1

The time of motion of the coin is determined as t = √(0.204x).

The time of motion of an object or a projectile is the time taken for the objects to travel from its initial position to the final position.

The time taken for the coin to fall from the given height "x" is calculated as follows;

h = vt + ¹/₂gt²

where;

x = 0 + ¹/₂gt²

2x = gt²

t² = 2x/g

t = √(2x/g)

t = √(2x/9.8)

t = √(0.204x)

Thus, the time of motion of the coin is determined as t = √(0.204x)

Learn more about time of motion here: https://brainly.com/question/2364404

#SPJ1

The description of water pollution and it's likely causes in Florida can be found below.

Water pollution is the contamination of water, especially surface water, by sewage effluent, fertilizer runoff, industrial chemical discharge etc.

These contaminants are called pollutants and when released into a body of water can deteriorate water quality and hamper its usage by humans.

Water pollution in Florida or any other developed state/country of the world can be caused by the following:

Learn more about water pollution at: https://brainly.com/question/19920929

#SPJ1

Given the flow of current and the voltage, the resistance of the lamp is 80 Ohms.

Ohm’s law states that the potential difference between two points is directly proportional to the current flowing through the resistance.

V = IR

Where V is the voltage or potential difference, I is the current and R is the resistance.

Given the data in the question;

Plug the given values into the equation above and solve for R.

V = IR

120 = 1.5 × R

R = 120/1.5

R = 80Ω

Given the flow of current and the voltage, the resistance of the lamp is 80 Ohms.

Lear more about ohm's law here: https://brainly.com/question/12372387

#SPJ1

Answer:

80 is the answer

Explanation:

A cube of brass is ((density = 8.74g/cm³) .The height of the cube after calculating the given details is  2.15443 cm.

Due to differences in density, two identically sized cubes constructed of different materials will typically not weigh the same when compared when weighed. Additionally, it implies that a massive Styrofoam cube can have the same weight as a tiny lead cube. Platinum, lead, iron, and other dense materials are a few examples

Density = 8.74 g/cubic cm

mass = 87.321 gms

Density = mass / volume

volume = mass / density = 9.99096109 cubic cm ≈ 10 cubic cm

side of cube = ∛10 cm = 2.15443 cm

∴ height of cube = 2.15443 cm .

learn more about density here :

brainly.com/question/15164682

#SPJ9

The length of the skid marks is 136m.

Speed is the time charge at which an object is moving alongside a path, whilst pace is the price and direction of an item's movement. The rate of change of role of an item in any route. speed is measured because of the ratio of distance to the time in which the space changed into included.

calculation,

mass of car = 1900kg

speed = 14 m/s

F = ma

a = F(friction) / m

F(friction) = mu F(normal)

F(friction) = mu g m

a = mu g m / m

a = mu g

a = 0.6 * 9.81m/s²

a = 5.886 m/s²

v² = 2 a x

x = v² / 2 a

x = (40m/s)²/ 2 * 5.886m/s²

x = 136m

Speed is a way of measuring how quickly something is shifting or being executed, or something moving rapidly. Speed is described because of the charge of trade of distance with time. It has the dimension of distance by time. therefore, the SI unit of pace is given as the aggregate of the simple unit of distance and the primary unit of Time. for this reason, the SI unit of velocity is a meter in step 2d. the rate of a body is converting with appreciation to time it's far shifting with a non-uniform velocity.

Learn more about speed here:-https://brainly.com/question/13943409

#SPJ1

John Deere, a U.S. company, sells a tractor to a farmer in Canada. It is a  GDP category is net exports.

Farmers are the person who usually cultivates and grows crops. They often also have cattle farming also. These farmers earn money by selling the crops in the market.

As a person is exporting goods and services to the US market, then we can say that the person is an exporter of court. There is GDP which is gross domestic product the US company that sells the status to Canada will be termed as the net exporter and represented over in that category.

Learn more about farmers, here:

https://brainly.com/question/18390861

#SPJ1

Answer: Vx= 86.6 m/s & Vy= 50 m/s

Explanation:

Vx= 100*cos30° = 86.6 m/s

Vy= 100*sin30° = 50 m/s

The correct answer is 54.6 min.

Running speed of Ilya and Anya is v_r=7.50 mi/hr

Walking speed of Ilya and Anya is v_w=3.50 mi/hr

Total length of the route is d=5.00 miles.

Total time taken by Anya to cover the distance is

[tex]t_A= d/2/v_r+ d/2/v_w[/tex]

[tex]t_A= d/2v_r + d/2v_w[/tex]

[tex]t_A=d/2 \times1/v_r +1/v_w[/tex]

[tex]t_A= d/2 \times v_r+v_w / v_rv_w[/tex]

[tex]t_A[/tex]= 5.00/2 × 7.50+3.50/7.50 × 3.50 hr

[tex]t_A[/tex]= 5.00/2 × 11/26.25 hr

[tex]t_A[/tex]= 55/52.5 hr

[tex]t_A[/tex]=1.05 hr

Therefore Anya will take 1.05 hr to cover the distance.

Average speed of Anya is

[tex]v_{avg} = d/t_A[/tex]

[tex]v_{avg}[/tex]= 5.00/1.05 mi/hr

[tex]v_{avg}[/tex] = 4.76 mi/hr

Therefore Anya's average speed is 4.76 mi/hr.

If total time taken by Ilya to cover the distance is t , then

([tex]v_r[/tex] × t/2+(v_w × t/2=d))

t/2 × ([tex]v_r+v_w[/tex])=d

t × ([tex]v_r+v_w[/tex])=2d

t = 2d/([tex]v_r+v_w[/tex])

t = 2 × 5.00/7.50+3.50

t = 10/11 hr

t = 0.91 × 60 min

t = 54.6 min

Therefore total time taken by Ilya to cover the distance is 54.6 min.

To learn more about average speed refer the link:

https://brainly.com/question/14782441

#SPJ9

You are traveling up on an elevator to the 95th floor of the Hancock tower. As it nears the 95th floor, your weight appears to be lighter.

Here is an exercise in thought. Consider a container with internally completely reflecting surfaces that is partially filled with light and located at sea level on Earth. The light will be somewhat gravitationally redshifted as it ascends, which will cause it to reflect at the top of the container with a little less momentum. Similar to how it will be blue shifted when travelling downward and give the container's bottom greater momentum. Weight is a quality of something that is subject to gravity. Light is drawn to objects with mass by gravity because it has energy. Since two photons (separate "pieces" of light, in a broad sense) have energy, I imagine they would be attracted to one another gravitationally. However, it would be really little.

Learn more about energy here-

https://brainly.com/question/1932868

#SPJ9

A neutralization reaction is when an acid and a base react to form water and a salt and involves the combination of H+ ions and OH- ions to generate water.

Answer:

see below

Explanation:

1 139 m / 37 s = 30.784 m/s   South

A car is traveling due north at 23.6 m>s.

Find the velocity of the car after 7.10 s if its

acceleration is

The acceleration is known to be: a(t) = 1.7 m/s2.

We must integrate over time to obtain the velocity function, and the results are:

v(t) = (1.7m/s^2)

*t + v0

If we suppose that we begin at 23.6 m/s, then the initial velocity is: v0 = 23.6 m/s, where v0 is the beginning velocity.

The velocity formula is then: v(t) = (1.7m/s2).

*t + 23.6 m/s

We now seek to determine the value of t such that v(t) = 27.8 m/s.

Consequently, v(t) = 27.8 m/s = (1.7 m/s2)

*t + 23.6 m/s = (1.7 m/s2) 27.8 m/s - 23.6 m/s

t = 2.5 seconds when *t 4.2 m/s = (1.7 m/s/2)

At such acceleration, 2.5 seconds are required.

To learn more about acceleration Visit :

https://brainly.com/question/19599982

#SPJ9

The magnitude and direction of resultant force is 4.12N and direction is 75.96degree

The combined force that affects a body in a different way is known as the resultant force. Typically, it uses a vector calculation to calculate.

F net = / (square root of F1 resultant + F2 resultant + F1F2 cos tita)/........(1)

For instance, if two forces are acting in the same direction, we add them together; if they are acting in opposition, we subtract them from one another.

When two forces are exerting pressure on a body at an angle of, the combined net force is 4N in the direction of North. In this case, the two forces are 10N and 6N, which are operating in opposing directions. Additionally, 5N and 4N are moving in the other direction, resulting in a net force of 1N moving westward from these two forces.

by substituting we get F net =4.12N

direction is = 4 / tan tita = 75.96 degree

To learn more about force:

https://brainly.com/question/13191643

#SPJ9

Answer:

The ball accelerates because of gravity which is constant. So we can apply one of the equations of uniformly accelerated motion to solve the problem.

[tex]Vf^2=Vo^2+2aS\\[/tex] is compatible since [tex]S, Vo, a[/tex] are given enabling us to calculate [tex]Vf[/tex] .

[tex]Vf^2=(0m/s)^2+2*10m/s^2*37m\\Vf^2=20m/s^2*37m\\Vf^2=740m^2/s^2\\Vf=\sqrt{740} m/s\\ Vf=27.202941017 m/s\\[/tex]

awnser D. 1600 mA

Explanation:

Ns/Np=Ip/Is

current is inverse

100/800=200/x

100x=160000

x=1600

When using association to store and remember information, you are also encoding.

When trying to store and remember information, the following stages take place in order:

Storing a memory trace is called as encoding. Perception leaves representation in memory. It is the conversion of information for storage purposes.

Therefore, when using association to store and remember information, you are also encoding.

To know more about Associative memory

https://brainly.com/question/2602585

#SPJ1

The calculated angle is 305° and if v=a,b is the position vector, then |v|=a²+b² is the calculated magnitude.

If v=a,b is the position vector, then |v|=a²+b² will give the magnitude. Depending on the application, the direction is equal to the angle made with the x-axis or the y-axis. The formula tan=(ba)=tan1 determines the direction of a position vector (ba), We may say that the vector must be inclined in the fourth quadrant in this case because the vector's x and y components are both positive.

Consequently, the angle must be greater than 270 degrees and less than 360 degrees.

Now, in order to determine the value, we can say that

tanθ=opposite side/adjacent side

=8.6/6.1

=tan⁻¹1.41

=54.65, which indicates that it is inclined at an angle above with the X axis in the fourth quadrant (360-54.65 = 305.6°).

Consequently, the proper response will be 305° degrees if the angle is measured counterclockwise.

Learn more about vector here-

https://brainly.com/question/13322477

#SPJ4

The x and y component of the dog's velocity at  t₂ = 25.0 s is 7.53 m/s and 2.933 m/s respectively.

The magnitude of the dog's velocity is 8.076 m/s.

The velocity components of a dog running in an open field are:

[tex]v_{x}=2.8 {~}m/s\\v_{y}=-1.8{~}m/s[/tex] at t₁ = 12 sec.

The average acceleration of the dog in the time interval t₁ = 12 sec to t₂ = 25 sec is 0.45 m/s² and the direction 36°.

(A) The x component of the dog velocity at t₂ = 25 sec will be:

Vₓ = vₓ + aₓ(cos(36)) × (t)

Vₓ = 2.8 + ( 0.45) × (0.89) × ( 25 - 12 )

Vₓ = 2.8 + 4.7327

Vₓ = 7.53 m/s

(B) The y component of the dog's velocity at t₂ = 25 sec will be:

[tex]V_y=v_y+a_y(cos(\theta))t\\V_y=-1.8+(0.45)(cos(36))(25-12)\\V_y=-1.8+4.7327\\V_y=2.933{~}m/s[/tex]

(C) Therefore, the magnitude of the dog's velocity is:

[tex]V=\sqrt{(v_x)^{2}+(v_y)^{2}}\\V=\sqrt{(7.53)^{2}+(2.93)^{2}}\\ V=\sqrt{56.7+8.58}\\ V=\sqrt{65.28}\\ V=8.0796{~}m/s[/tex]

Learn more about velocity here:

https://brainly.com/question/80295

#SPJ9

The complete question is mentioned below:

A dog running in an open field has components of velocity vₓ = 2.8 m/s and [tex]v_y = -1.8{~} m/s[/tex] at time t₁ = 12.0 s. For the time interval from t₁ = 12.0 s to t₂ = 25.0 s, the average acceleration of the dog has a magnitude of 0.45 m/s² and a direction of 36.0° measured from the +x-axis toward the +y-axis.

(A) At time t₂ = 25.0 s, what is the x-component of the dog's velocity?

(B) At time t₂ = 25.0 s, what is the y-component of the dog's velocity?

(C) What is the magnitude of the dog's velocity?

Recording a change in color would be an example of a qualitative observation and is therefore denoted as option B.

This is referred to as the type of observation which is characterized by the use of our senses such as sight, smell etc while on the other hand quantitative observation has to do with measurement of different types of number variables and parameters

Color was chosen as the most appropriate choice because it doesn't deal with numbers and it can be felt with the use of our sense of smell which is present in the nose of individuals.

Read more about Qualitative observation here https://brainly.com/question/13676604

#SPJ1

Answer:

The direction of the velocity vector is upward and the direction of the acceleration vector is downward. A ball thrown straight upward moves initially with a decreasing upward velocity.

Explanation:

The radius of the disc will be 0.496 meters.

The pace at which an object rotates or revolves around an axis is known as its angular velocity. The Greek letter omega stands for angular velocity. Because it is expressed as an angle per unit of time, angular velocity in the SI is measured in radians per second. [[tex]M^{0}L^{0}T^{-1}[/tex]] is the dimensional formula for angular velocity.

According to the question, the given values are :

Acceleration, a=4.9 m/s² and,

Period of rotation, T=2.0 seconds

So, angular velocity (ω) of disc =2π/T

⇒2π/2

= π rad/sec.

Acceleration= rω²

4.9= r×π²

r=0.496 meters.

Hence, the radius of the disc will be 0.496 meters.

For more information about Angular velocity :

https://brainly.com/question/12446100

#SPJ1

The distance traveled in meters is 290m. It can be solved using Newton's Laws of motion.

You can solve this problem by using the formula of

d = 1/2 a t^2

where d is the distance traveled in meters,

a = 20 m/s², and t =7 seconds

Plug-in the data to the formula and solve for the distance traveled after

7 s.

d = 1/2 a t^2

=1/2 × 20 × 7²

= 290m

Hence the dist travelled by the car is 290m

Learn more about distance here

https://brainly.com/question/23848540

#SPJ9

Answer:

t = 10/9.81 = 1.02s

Explanation:

the ball will be up in the air for 1.02 seconds

Kenny’s ideas and their acceptance were due to open-mindedness because she led to the use of hot baths and exercise to treat polio victims.

Elizabeth Kenny was a world-renowned nurse from Australia who develop a treatment for poliomyelitis, a very serious viral disease caused by poliovirus.

Elizabeth Kenny's ideas were controversial because they may be considered to be against conventional medical treatments.

In conclusion, Kenny’s ideas and their acceptance were due to open-mindedness because she led to the use of hot baths and exercise to treat polio victims.

Learn more about Elizabeth Kenny here:

https://brainly.com/question/10653494

#SPJ1

When the length of the pendulum in pendulum clock increases by 0.1 % , then the error in time per day is c) 43.2s

Let the pendulum = L

The time in a day will be: = 60 × 60 × 24

When the length is increased, the new length will be:

= L + 0.001L

New time period will be:

T =✓0.001s

Now, the error in a day will be:

= ✓0.001 × 60 × 60 × 24 - 1 × 60 × 60 × 24.

= 60 × 60 × 24(✓1.001 - 1)

= 43.2 seconds.

Therefore, the correct option is C.

Learn more about time on:

brainly.com/question/10428039

#SPJ1

Answer:

Time difference = T1-T2 = D1/V1-D2/V2 = D ( 1/V1-1/V2)

Time difference = 5.5 min = 5.5*60=330 sec, V1 = .09 m/s, V2= 1.9 m/s

330 = D (1/.9 – 1/1.9)

330= D(1.11-.5263)

330=D(.585)

D= 330/.585 = 564.3 m

Explanation:

The magnitude of the change in velocity is determined as 408.94 km/h.

The change in direction of the velocity is 64.4⁰ north of west.

The magnitude of the average acceleration during the trip is 0.0105 m/s².

The magnitude of change in velocity is the resultant velocity of the plane.

v² = a² + b² - 2ab cosθ

where;

v² = (192²) + (250²) - 2(192 x 250) cos(135)

v² = 167,236

v = √167,236

v = 408.94 km/h

vyi = 192 km/h

vy2 = 250 x sin(45) = 176.77 km/h

vy(total) = 192 km/h + 176.77 km/h = 368.77 km/h

vxi = 0

vx2 = - 250 km/h x cos(45) = -176.77 km/h

θ = arc tan (Vy/Vx)

θ = arc tan(368.77 / -176.77)

θ = -64.4 ⁰

θ = 64.4⁰ north of west.

a = v/t

v = 408.94 km/h = 113.6 m/s

h = 3 h = 10,800 seconds

a = (113.6 m/s) / ( 10,800 s)

a = 0.0105 m/s²

Learn more about change in velocity here: https://brainly.com/question/25749514

#SPJ1