g uppose that 3 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 45 cm. (a) How much work is needed to stretch the spring from 35 cm to 37 cm? (Round your answer to two decimal places.) .02 Incorrect: Your answer is incorrect. J (b) How far beyond its natural length will a force of 10 N keep the spring stretched? (Round your answer one decimal place.)

Answer:

Explanation:

If Two cylindrical resistors are made from the same material, then their resistivity will be the same.  Formula for calculating resistivity of a material is expressed as;

[tex]\rho = \frac{RA}{L} \ where \ A = \frac{\pi d^2}{4}[/tex] where;

R is the resistance

A is the cross sectional area of the material

L is the length of the material

For the shorter cylinder:

Length = L

diameter = D

[tex]\rho = \dfrac{R_s(\frac{\pi D^2}{4})}{L} \\\\\rho = \dfrac{R_s{\pi D^2}}{4L}[/tex]

For the longer cylinder:

Length = 16L

diameter = 4D

[tex]\rho = \dfrac{R_l(\frac{\pi (4D)^2}{4})}{16L} \\\\\\\rho = \dfrac{R_l(\frac{\pi (16D^2)}{4})}{16L} \\\\\rho = \dfrac{R_l{16\pi D^2}}{16L}\\\\\rho = \dfrac{R_l{\pi D^2}}{L}[/tex]

Since their resistivity are the same then;

[tex]\dfrac{R_s{\pi D^2}}{4L} = \dfrac{R_l{\pi D^2}}{L} \\\\ \dfrac{R_s}{4} = {R_l} \\\\R_s = 4R_l\\\\R_l = \frac{R_s}{4}[/tex]

Hence the resistance of the longer resistor is a quarter of the shorter resistor.

Answer:

This measurement would be a measure of the speed of an object(the car ) in motion

Explanation:

A driver looks down at their speedometer and sees they are moving at 45 mph. This measurement would be about the speed of the car or about how fast the car is moving.

This means, the car is travelling the distance of 45 miles in every hour.

This measurement would also be about the instantenous speed of the car which is 45mph.

Answer:

The hight of the building is 38.16 m

Explanation:

These two pieces of information given, first, the watermelon is 30 m  above the ground and after 1.50 s the watermelon has been spotted. Now we are required to find the height of the building.

Use the below formula to find the height of buildings.

S = ut + ½ gt^2

30  =1.5u + (1/2) × 9.8 (1.5)^2

u = 12.65 m/sec

v^2 – u^2 = 2gs

(12.65)^2 = 2×9.8 s’

S’ = 8.16 m  

h = s + s’

h = 30 + 8.16 = 38.16 m

The hight of the building is 38.16 m.

The height of the building is 38.16 m.

Given data:

The height above the ground is, h = 30.0 m.

The time interval after observation of first spot is, t = 1.50 s.

We need to find the height of building. And since two pieces of information given, first, the watermelon is 30 m  above the ground and after 1.50 s the watermelon has been spotted. So, using the second kinematic equation of motion as,

[tex]h = ut + \dfrac{1}{2}gt^{2}[/tex]

Here, u is the initial speed. Solving as,

[tex]30 = (u \times 1.50) + \dfrac{1}{2} \times 9.8 \times (1.50)^{2}\\\\u =12.65 \;\rm m/s[/tex]

Now landing distance (s') is calculated using the third kinematic equation of motion as,

[tex]v^{2} =u^{2}+2(-g)s\\\\0^{2} =12.65^{2}+2(-9.8)s\\\\s = 8.16 \;\rm m[/tex]

Then the height of building is given as,

H = h + s

H = 30 m + 8.16 m

H = 38.16 m

Thus, we can conclude that the height of the building is 38.16 m.

Learn more about the kinematic equations of motion here:

https://brainly.com/question/16556016

Answer:

The magnetic field is zero at a radius r = 4 cm.

Explanation:

The magnetic field due to the wire is given by B₁ = μ₀I₁/2πr where I₁ = current in wire = 1 A and r = distance of point where magnetic field is zero from wire.

Now, since the current is uniformly distributed in the cross section of the cylinder, its current density is constant.

So, with current I₂ = 9 A flowing in the cylinder and radius, a = 12 cm. Let I' = current at radius r where the magnetic field is zero. So,

I'/πr² = I₂/πa²

I' = I₂r²/a²

Using Ampere's Law, the magnetic field B₂ at the distance r is given by

∫B.ds = μ₀I'

∫Bdscos0 = μ₀I' (since the magnetic field is parallel to the path)

B∫ds = μ₀I'   ∫ds  = 2πr

B2πr = μ₀I'

2Bπr = μ₀I₂r²/a²

B₂ = μ₀I₂r/2πa²

So, when the net magnetic field is zero, B₁ = B₂

So,  μ₀I₁/2πr = μ₀I₂r/2πa²

I₁/r = I₂r/a²

I₁/I₂ = r²/a²

r² = I₁/I₂a²

taking square root of both sides,

r = a√(I₁/I₂)

substituting the values of the variables, we have

r = 12√(1/9)

r = 12/3

r = 4 cm

The magnetic field is zero at a radius r = 4 cm.

Answer:

Explanation:

The question is incomplete. Here is the complete question.

A ball with mass m kg is thrown upward with initial velocity 22 m/s from the roof of a building 17 m high. Neglect air resistance. Use g=9.8 m/s2. Round your answers to one decimal place. (a) Find the maximum height above the ground that the ball reaches. xmax= meters (b) Assuming that the ball misses the building on the way down, find the time that it hits the ground.

a) Using the equation of motion formula;

v² = u²+2gH where;

u is the initial velocity

v is the final velocity

theta is the angle of launch

g is the acceleration due to gravity.

H is the maximum height reached by the ball

Since the ball is thrown upwards, the acceleration due to gravity will be negative. The equation then becomes;

v² = u²-2gH

Given

v = 0m/s

u = 22m/s

g = 9.8m.s²

0² = 22²-2(9.8)H

-22² = -19.6H

H = -22²/-19.6

H = 24.69m

If the biuliding is 17m high, the maximum height above the ground that the ball reaches will be;

Hmax = 24.69+17

Hmax = 41.69m

b) The time it takes to hit the ground can be expressed using the formula

v = u-gt

0 = 22-9.8t

-22 = -9.8t

t = -22/9.8

t = 2.45secs

Hello ┬┴┬┴┤◕3◕)づ├┬┴┬┴

The answer is 3 m

the gap in between 4s and 6s is 5s

you follow your finger up to the purple like, and follow the purple line in a straight line to the left. It ends at 3m and that is your answer.

Explanation:

Equation for Impact

FΔt = ΔP,

F = force

Δt  = Impact of time

ΔP = Change in momentum

Car steering is engineered to fail in order to maximize the time of contact and hence reduce the initial impact and mitigate the damage incurred.

Road guard railing crumple on contact to maximize impact time and hence reduce impact intensity and mitigate damage.

Road safety containers are loaded with liquid or sand as they improve the period of impact.

Answer:

The velocity when the runner stopped is v =0 m/s

The acceleration is [tex]a = 0.4 \ m/s [/tex]

Explanation:

From the question we are told that

The initial velocity is [tex]u = 2 \ m/s[/tex]

The time taken is [tex]t = 5 \ s[/tex]

Generally from the question we are told that the person stopped running so the person velocity at that moment is v =0 m/s

Now the acceleration is mathematically represented as

[tex]a = \frac{v - u}{t}[/tex]

=> [tex]a = \frac{0 - 2}{5}[/tex]

=> [tex]a = 0.4 \ m/s [/tex]

The question is incomplete; However, the height from which the stone is thrown is most likely to be what's required of the question

Answer:

See Explanation

Explanation:

Given

[tex]Initial\ Speed, u = 12.0m/s[/tex]

[tex]Time, t = 1.54\ s[/tex]

Required

Determine the height

This question will be answered using the following equation of motion;

[tex]S = ut + \frac{1}{2}gt^2[/tex]

Take g as 9.8

This gives:

[tex]S = 12 * 1.54 + \frac{1}{2} * 9.8 * 1.54^2[/tex]

[tex]S = 12 * 1.54 + \frac{1}{2} * 9.8 * 2.3716[/tex]

[tex]S = 18.48 + 11.62084[/tex]

[tex]S = 30.10084[/tex]

[tex]S = 30.1\ m[/tex] (Approximated)

Hence; Height = 30.1m

Answer:

18.3 C

Explanation:

Answer: 55/3 °C

Explanation:

Formula:

C=5/9(F-32)

Given:

F=65

Solve:

C=5/9(F-32)

C=5/9(65-32)

C=5/9(33)

C=55/3

Answer: Bohr developed the Bohr model of the atom, in which he proposed that energy levels of electrons are discrete and that the electrons revolve in stable orbits around the atomic nucleus but can jump from one energy level (or orbit) to another. ... During the 1930s Bohr helped refugees from Nazism.

Answer:

Resultant = 13km

Direction = 67.38° East of North

Explanation:

Given the following :

5km North ; 12km East

Resultant Displacement (r) :

r² = 5² + 12²

r² = 25 + 144

r² = 169

r = √169

r = 13

Direction:

Tangent = opposite / Adjacent

Tanθ = opposite / Adjacent

Opposite = 12 ; adjacent = 5

Tanθ = (12/5)

Tanθ = 2.4

θ = tan^-1(2.4)

θ = 67.38° east of north

Answer:

B

Explanation:

The answer should be B.

Answer:

We use pythagorean theorem

So that

r = √(x² + y²)

r = √(94.8)² + (-149)² )

r =√ 9682.6 + 22201

= 178.6

direction we use

စ = tan^-1(98.4/149)

= tan^-1 (0.6604)°

Answer:

(a) , .  and .

(b)[tex]\vec A - \vec C=22 \hat i -10 \hat j[/tex].

(c)[tex]|\vec A - \vec B|=63.13[/tex] and the direction [tex]\theta =[/tex] 124.56°.

Explanation:

Given that,

,

and

[tex]\vec {C}=2 \hat i +43 \hat j[/tex]

(a) The magnitude of a vector is the square root of the sum of the square of all the components of the vector, i.e. for a ,.

So, the magnitude of the is

[tex]|\vec A|=\sqrt {24^2+ 33^2}[/tex]

[tex]\Rightarrow |\vec A|=\sqrt {1665}[/tex]

.

The magnitude of the is

[tex]|\vec B|=\sqrt {55^2+ (-12)^2}[/tex]

[tex]\Rightarrow |\vec B|=\sqrt {3169}[/tex]

.

And, the magnitude of the is

[tex]|\vec C|=\sqrt {2^2+ 43^2}[/tex]

[tex]\Rightarrow |\vec C|=\sqrt {1853}[/tex]

.

(b) The difference between the two vectors is the difference between the corresponding components of the vectors. So, the required expression of is

[tex]\vec A - \vec C=(24 \hat i +33 \hat j) - (2 \hat i +43 \hat j)[/tex]

[tex]\Rightarrow \vec A - \vec C=24 \hat i +33 \hat j - 2 \hat i -43 \hat j[/tex]

[tex]\Rightarrow \vec A - \vec C=22 \hat i -10 \hat j[/tex]

(c) The expression of is

[tex]\vec A - \vec N=(24 \hat i +33 \hat j) - (55 \hat i -12 \hat j)[/tex]

[tex]\Rightarrow \vec A - \vec B=24 \hat i +33 \hat j - 55\hat i +12 \hat j[/tex]

[tex]\Rightarrow \vec A - \vec B=-31 \hat i +45 \hat j\;\cdots (i)[/tex]

The magnitude of is

[tex]|\vec A - \vec B|=\sqrt {(-31)^2+55^2}[/tex]

[tex]\Rightarrow |\vec A - \vec B|=\sqrt {3986}[/tex]

[tex]\Rightarrow |\vec A - \vec B|=63.13[/tex]

Now, if a vector [tex]\vec V= -\alpha \hat i +\beta \hat j[/tex] in 3rd quadrant having direction [tex]\theta[/tex] with respect to [tex]\hat i[/tex] direction, than

in the anti-clockwise direction.

Here, from equation (i), for the vector [tex]\vec A - \vec C[/tex], [tex]\alpha=31[/tex] and [tex]\beta=45[/tex].

[tex]\Rightarrow \theta = \pi-\tan ^{-1}\left(\frac {45}{31}\right)[/tex]

180°-55.44° [as \pi radian= 180°]

124.56° in the anti-clockwise direction.

(d) Vector diagrams for [tex]\vec A +\vec B[/tex] and [tex]\vec A - \vec B[/tex] has been shown  

in the figure(b) and figure(c) recpectively.

Vector [tex]\vec A - \vec B[/tex] is in 3rd quadrant as calculated in part (c).

While Vector [tex]\vec A +\vec B=(24 \hat i +33 \hat j)+(55 \hat i -12 \hat j)[/tex]

[tex]\Rightarrow \vec A +\vec B=79 \hat i +21 \hat j[/tex], which is in 1st quadrant as both the components are position has been shown in figure(b).

The average speed is 1/2 m/s.

To determine the answer, we need to know about average speed.

Distance covered by an object per unit time is known as average speed.

Mathematically, average speed= Total distance travelled/ total time taken

Here, total distance travelled = 10m,

         total time taken = 20s

 Average speed = 10/20 = 1/2 m/s

Thus, we can conclude that the average speed is 1/2 m/s.

Learn more about average speed here:

https://brainly.com/question/4931057

#SPJ2

Answer:

The new period will be reduced by 50%

Explanation:

The period of pendulum is given by;

[tex]T= 2\pi\sqrt{\frac{L}{g} }\\\\\frac{T}{2\pi} = \sqrt{\frac{L}{g} }\\\\(\frac{T}{2\pi} )^2 = {\frac{L}{g}}\\\\\frac{T^2}{4\pi ^2} = {\frac{L}{g}}\\\\T^2(\frac{g}{4\pi ^2}) = L\\\\ \frac{g}{4\pi ^2}= \frac{L}{T^2}\\\\\frac{L_1}{T_1^2} = \frac{L_2}{T_2^2}[/tex]

When the length is decreased by 25%, the new length L₂ is given by;

L₂ = 25/100(L₁)

L₂ = 0.25L₁

[tex]\frac{L_1}{T_1^2} = \frac{L_2}{T_2^2}\\\\T_2^2 = \frac{T_1^2L_2}{L_1} \\\\T_N^2 = \frac{T^2(0.25L_1)}{L_1}\\\\ T_N^2 =0.25T^2\\\\T_N = \sqrt{0.25T^2}}\\\\T_N = 0.5 T[/tex]

Thus, the new period will be reduced by 50%

Answer:

28km/h

Explanation:

92km = 4 hours

176 - 92 = 84

84km = 3 hours

84/3 = 28

28km/h

Hopefully this helps you :)

pls mark brainlest ;)

Answer:

Explanation:

a) because it's immoral as you're trying to convince people of your views when you should be giving both sides of the story so people are able to come up with their own opinions on what you're talking about

Answer:

000000000000000000000000000

Answer:

1.73 m/s²

Explanation:

Given:

Δx = 250 m

v₀ = 0 m/s

t = 17 s

Find: a

Δx = v₀ t + ½ at²

250 m = (0 m/s) (17 s) + ½ a (17 s)²

a = 1.73 m/s²

The acceleration of this object is 1.730 meter per seconds square.

Given the following data:

To find the acceleration of this object, we  would use the second equation of motion.

Mathematically, the second equation of motion is given by the formula;

[tex]S = ut + \frac{1}{2} at^2[/tex]

Where:

Substituting the given values into the formula, we have;

[tex]250 = 0(17) + \frac{1}{2} (a)(17^2)\\\\250 = \frac{1}{2} (289)a\\\\250 = 144.5a\\\\a = \frac{250}{144.5}[/tex]

Acceleration, a = 1.730 [tex]m/s^2[/tex]

Therefore, the acceleration of this object is 1.730 meter per seconds square.

Read more: https://brainly.com/question/7998145

Answer:

The answer is

Explanation:

To calculate the work done by a body we use the formula

From the question

force = 10 N

distance covered = 1.5 m

So the work done is

work done = 10 × 1.5

We have the final answer as

Hope this helps you

Answer:

18*10^10 meters

Explanation:

V= d/t         10 mins = 600 seconds

3*10^8 = d/600s

(3*10^8)*(6*10^2) = d

d = 18*10^10 m

Answer:

3.6s

Explanation:

Have In mind that the sports car will catch up with bus when their positions are equal

So

S = ut + 1/2at²

where u is initial velocity

For sports car we have

x = 0 + 1/2 x 9 x t²

For Bus

S= 16ts + 0

Equating the two

1/2 x 9 x t² = 16t

4.5 x t = 16

t = 3.6s

Answer:

Explanation:

If a positive charge enters a magnetic field at 90 degrees the charge is deflected in a circular path by a force that acts perpendicular to it in line with Flemings right-hand rule

to derive the radius of the path of the charge we apply

F= mv^2/r=Bev

where

m= mass of the electronic charge

e=charge

B=magnetic field

v=average speed

r=radius

rearranging we have

r=mv^2/Bev

r=mv/Be

Answer:

A- 12 km

B- 42 minutes

C- 17.14 km per hour

Explanation:

A- The displacement of the total trip is 12 kilometers, which emerges by adding the 10 kilometers traveled by car to the 2 kilometers traveled on foot.

B- The trip, in total, took 42 minutes, which arises from adding the 30 minutes of the journey on foot, plus 12 minutes of travel by car at 72 km / h (72/60 x 10 = 12).

C- While 12 km were covered in 42 minutes, the average speed of the trip was 17.14 km / h. This arises from the following calculation:

42 = 12

60 = X

(60 x 12) / 42 = X

17.14 = X

Answer:

V=u+at

=4+4*2.5

=14m/s

Explanation:

Initial velocity =4m/s

acceleration =4m/(second) squared

time =2.5 seconds

v=u+at

v=4+4*2.5

v=14m/s

Answer:

A. Dependent variable

Explanation:

In a graph showing how temperature of a material changes over time, temperature is taken on y-axis and time is taken on x-axis. It shows how temerature altered as the time changes.

In temperature-time graph, temperature is directly dependent on time. With the increase in time, temperature rises, falls or remains constant. It implies that temperature is dependent variable that depend on time.

Hence, the correct option is (A).