5. A combination of waves is producing oscillations on a rope that is fixed at both ends and has a tension of 100 ????. The wavelength of the resulting net wave is equal to the length of the rope. If the equation for the displacement of a point on the rope is given by y(x, t) = (0.1 m) sin π x sin 12πt, where the rope begins at x = 0, x is in meters, and t is in seconds, what are the a) length of the rope, b) the speed of the waves on the rope, and c) the mass of the rope?

Answer:

Answer:

The x - intercept is 1/3

The y - intercept is 1/2

The gradient is -3/2

Explanation:

To find the x - intercept of the equation 2y + 3x = 1, we find the value of x when y = 0. So,

2y + 3x = 1

2(0) + 3x = 1

0 + 3x = 1

3x = 1

x = 1/3

So, the x - intercept is 1/3

To find the y - intercept of the equation 2y + 3x = 1, we find the value of y when x = 0. So,

2y + 3x = 1

2y + 3(0) = 1

2y + 0 = 1

2y = 1

y = 1/2

So, the y - intercept is 1/2

To find the gradient of the equation 2y + 3x = 1, we re-write it in gradient intercept form by making y subject of the formula.

So, 2y + 3x = 1

2y = -3x + 1

y = -3x/2 + 1/2

The coefficient of x which equals -3/2 is the gradient.

The gradient is -3/2

Answer:

Given that;

Number of turns in the solenoid N = 310

Length of the solenoid L = 18 cm = 0.18 m

Radius of the solenoid r = 1.60 cm = 0.016 m

Current in the first Circuit I₁ = 1.90A

Number of turns in second coil N₂ = 4

Final Current solenoid I₂ = 5.0 A

Time interval to change the time Δt = 0.9 s

a)

According to Ampere's law, magnetic field inside a conductor is calculated as;

B₁ = ц₀N₁I₁ / L

(ц₀ = 4π × 10⁻⁷  constant)

therefore we substitute

{(4π × 10⁻⁷) ×  310 × 1.9A} / 0.18m

= 0.0041 T

b)

Magnetic field inside the solenoid after t = 0.9

B₁ = ц₀N₁I₂ / L

= {(4π × 10⁻⁷) ×  310 × 5.0A} / 0.18m

= 0.0108 T

c)

Area of coil is

A = πr²

A = π ×  ( 0.016 )²

A = 0.000804 m²

d)

Change in magnetic influx is

dФ = (B₂ - B₁) A

= ( 0.0108 T - 0.0041 T) × 0.000804 m²

= 0.0000053868 ≈ 5.39 × 10⁻⁶

e)

Average induced emf is

e = -N₂ ( dФ / dt )

e = ( -4 ) ( 5.39 × 10⁻⁶ / 0.9)

e = - 2.39 × 10⁻⁵V ( NOTE, this is not equal to the instantaneous induced emf )

f)

The induced emf is very low, so the contributions to the magnetic field in the coil is Negative.

Answer:

As rocket mass increases, acceleration decreases.

Explanation:

From Newton's second law of motion;

F= ma

Where;

m= mass of the object

a= acceleration of the object

Hence we can write;

a= F/m

This implies that an increase in mass (m) will lead to a decrease in acceleration if the force on the object is held constant.

Hence, if the rockets have different masses, they will have different accelerations.

Hello!

---------

As rocket mass increases, acceleration decreases.

Hope this helps! The rest are available on Quizlet at "Unit 6: Lesson 4 Force, Mass and Acceleration". Thanks and good luck!

Explanation:

current = velocity/resistance

I = V/R

15/4

current = 3.75A

hope this helps...

Answer:

D=M/V. That's the formula. Density is expressed, in cubic centimeters.

Explanation:

Answer:g/m³

g/cm³

-kg/L

-kg/cm³

Density in physics, is defined as the mass of the object over its volume. Density is considered as how much matter is contained in a single object by its volume or the matter that it occupies.

D = m / v

Explanation:

Answer:

9 kg

Explanation:

Momentum is mass times velocity.

p = mv

36 kgm/s = m (4 m/s)

m = 9 kg

The mass of the bicycle is 9 kg.

The momentum of the bicycle is the product of mass and velocity of the bicycle.

P = mv

where;

m = P/v

m = 36/4

m = 9 kg

Thus, the mass of the bicycle is 9 kg.

Learn more about momentum here: https://brainly.com/question/7538238

Answer:1860g

Explanation:The force would have to be greater than 1580g, which is when the student is pulling the sliding book with the spring scale

Answer:

The answer  is The acceleration is double its original value.

Explanation:

Hope this helps....

Have a nice day!!!!

Answer:

The acceleration is half of its original value

Explanation:

Answer:

Answer B is the correct answer: "Motion of one projectile as seen from the other is a straight line."

Explanation:

Let's write the equations of motion for each projectile, using that projectile [tex]a[/tex] is launched with velocity [tex]a[/tex] which has components associated with the angle of launching, given in x and y coordinates as: [tex]a_x\,\,and\,\,a_y[/tex].

Similarly, assume that projectile b is launched with velocity [tex]b[/tex] with components due to the launching angle = [tex]b_x\,\,and \,\,b_y[/tex]

then the equations of motion for the two projectiles launched at the same time (t) from the same spot (position that we assume to be at the origin of coordinates to simplify formulas) are:

[tex]x_a=a_x\,t\\y_a= a_y\,t-\frac{1}{2} g\,t^2\\and\\x_b=b_x\,t\\y_b= b_y\,t-\frac{1}{2} g\,t^2[/tex]

therefore, from the frame of reference of projectile "b", the x and y position of projectile "[tex]a[/tex]" would be:

[tex]x_{a\,b}= x_a-x_b= a_x\,t-b_x\,t=(a_x-b_x)\,t[/tex]  which is linear in "t"

[tex]y_{a\,\,b}=y_a-y_b= a_y\,t-\frac{1}{2} g\,t^2-\left[ b_y\,t-\frac{1}{2} g\,t^2\right]=(a_y-b_y)\,t[/tex] which is also linear in t.

Therefore the motion of one projectile with reference to the other is a straight line (answer B)

Notice as well that this two projectiles cannot collide because they have been launched together, and supposedly at different speeds and angles. The only way that they can share the same x-coordinate and the same y-coordinate at the same time "t" is if their velocity components are equal, which is not what we are told.

[tex]x_a=x_b\\a_x\,t= b_x\,t\\and\\y_a= y_b\\a_y\,t-\frac{1}{2} g\,t^2= b_y\,t-\frac{1}{2} g\,t^2\\a_y\,t=b_y\,t\\a_y=b_y[/tex]

Answer:

12.5 m/s

Explanation:

a = Δv / Δt

2.5 m/s² = Δv / 5 s

Δv = 12.5 m/s

Explanation:

Assuming the suitcase is near the surface of the earth, g = 9.8 m/s².

F = ma

F = (20 kg) (9.8 m/s²)

F = 196 N

Answer:

40 cm

Explanation:

Magnification of a pinhole camera is given by;

M= height of image/ height of object

Since;

M= 0.25

Height of image = 6cm

Height of object = height of image / M

Height of object = 6/0.25 = 24 cm

Height of image/ height of object = distance of image from pinhole/ distance of object from pinhole

Since the distance of image from pinhole = 10cm

Let the distance of object from pinhole be x

6/24 = 10/x

6x = 240

x= 240/6

x = 40 cm

Answer:

“They may feel colder but that's only an illusion,” Dr. Begley says. “Copper mugs actually absorb heat from the room faster than a glass.” Copper is an excellent thermal conductor, meaning it transfers heat from hot sources (like the room or your hand) to cold sources (like your drink) very efficiently.

Explanation:

Answer:

Upthrust = 20 N

Explanation:

The question says that "A body weighs 100N in air and 80N when submerged in water. Calculate the upthrust acting on the body ?"

Upthrust is defined as the force when a body is submerged in liquid, then liquid applies a force on it.

ATQ,

Weight of body in air is 100 N

Weight of body in water is 80 N

Upthrust is equal to the weight of body in air minus weight of body in water.

Upthrust = 100 N - 80 N

Upthrust = 20 N

So, 20 N of upthrust is acting on the body.

Answer:

230 = x + 105

x= 125

Explanation:

v = v0 + at

Answer:

The distance of the light is 9.4608 x 10^25 m

Explanation:

Time taken by the light = 10 billion years = 10 x 10^9 years

speed of light = 3 x 10^8 m/s

speed of light in m/years is = (3 x 10^8)/(60 x 60 x 24 x 365) = 9.4608 x 10^15 m/year

distance = speed x time

therefore, the distance of this light = 10 x 10^9 x 9.461 x 10^15 = 9.4608 x 10^25 m

Answer:  

more than 10 billion light years due to expansion of space

Explanation:

Answer:

5×10⁻⁸ m²

Explanation:

I assume you mean the resistivity of the material is 50×10⁻⁸ Ωm.

R = ρL/A

10 Ω = (50×10⁻⁸ Ωm) (1 m) / A

A = 5×10⁻⁸ m²

Answer:

The linear velocity of europe's motion in its orbit is 7875.58 km/hr.

Explanation:

Given that,

Time period of lo = 1.77 days

Time period of europa = 3.55 days

Distance of lo from jupiter = 421600 km

We know that,

Distance of europa from jupiter = 671000 km

We need to calculate the linear velocity of europe's motion in its orbit

Using formula of velocity

[tex]v=\dfrac{d}{t}[/tex]

Where, d = distance between europa and jupiter

t = time

Put the value into the formula

[tex]v=\dfrac{671000}{3.55\times24}[/tex]

[tex]v=7875.58\ km/hr[/tex]

Hence, The linear velocity of europe's motion in its orbit is 7875.58 km/hr.

Answer:

[tex]1.5 * 10^6[/tex]

Explanation:

Given

Digit: 1,500,000

Required

Represent using scientific notation

We start by expressing the given digit as a product of 1.5 and a multiple of 10

[tex]Digit = 1.5 * 1,000,000[/tex]

1,000,000 can be represented as 10⁶

So; the digit becomes

[tex]Digit = 1.5 * 10^6[/tex]

Hence, the scientific notation of 1,500,000 is 1.5 * 10⁶

Answer:

The pressure at the bottom of the river is less than that at the bottom of the lake.

Explanation:

From Bernoulli's equation, the pressure difference is given by

ΔP = ρgΔh + ρ(v₂² - v₁²)/2 where ρ = density of water, g = acceleration due to gravity, Δh = depth, v₁ = velocity at top, v₂ = velocity at bottom

For the lake, v₁ = v₂, since the velocity at the top and bottom are the same. So,

ΔP₁ = ρgΔh + ρ(v₁² - v₁²)/2 = ρgΔh + 0 = ρgΔh

P₂ - P₁ = ρgΔh

P₂ = P₁ + ρgΔh

For the river, v₁ < v₂, since the velocity at the top of the river is greater than at the bottom.

So,

ΔP₂ = ρgΔh + ρ(v₂² - v₁²)/2.

Since  v₁ < v₂, ρ(v₂² - v₁²)/2 will be negative,

So,

ΔP₂ = ρgΔh - ρ(v₂² - v₁²)/2.

Since ρ(v₂² - v₁²)/2 is negative, making ΔP less than that in the lake.

So, ΔP₂ = ΔP₁ -  ρ(v₂² - v₁²)/2.

ΔP₂ = P₃ - P₁

P₃ - P₁ = P₂ - P₁ -  ρ(v₂² - v₁²)/2.

P₃ = P₂ - ρ(v₂² - v₁²)/2.

where P₃ = pressure at bottom of the river and P₂ = pressure at bottom of the lake and P₁ = atmospheric pressure at top of river and lake respectively.

Since the factor ρ(v₂² - v₁²)/2 is removed from the pressure at the bottom of the lake, the pressure at the bottom of the river is therefore less than that at the bottom of the lake.

Answer:

=33 .3×10^6Ω

=33.3M Ω

Explanation:

We were told to calculate the Resistance value,

Given the heart pacemaker fires as 72 times a minute, which is the time constant

Then we can convert the pacemaker fires of 72 times a minute to seconds for unit consistency.

1 minutes= 60secs

Then ,Time constant τ=60secs/72=0.8333 seconds

Time constant τ can be calculated using the formula below

τ= RC

Where R= resistance

C = capacitance

Then making RESISTANCE subject of formula we have

R=τ/C

But Capacitance=25.0-nF = 25×10^25F

Substitute the values we have

R=0.833/25×10^25

=33 .3×10^6 Ω

But can still be converted to M Ω= 33.3M Ω

Therefore, the resistance is 33 .3×10^6 Ω or 33.3M Ω

NOTE: 1M= 10^6

The value of the resistance will be "3.33×10⁷ Ω".

According to the question,

Capacitor, C = 25.0 nF

60 sec - 72 fires

now,

Time for 1 fire,

[tex]t = \frac{60}{72}[/tex]

 [tex]= \frac{5}{6} \ sec[/tex]

Now,

⇒            [tex]V = V_0 (1-e^{-\frac{t}{RC} })[/tex]

     [tex]0.632 V_0=V_0(1-e^{\frac{-\frac{5}{6} }{R.25 n C} })[/tex]

[tex]e^{-\frac{1}{R\times 30\times 10^{-9}} } = 1-0.632 = 0.368[/tex]

                  [tex]= 2.72[/tex]

By taking "log" both sides,

⇒ [tex]ln \ e^{\frac{1}{R\times 30\times 10^{-9}} } = ln \ 2.72[/tex]

hence,

The Resistance be:

⇒ [tex]R = \frac{10^9}{30}[/tex]

       [tex]= 3.33\times 10^7 \ \Omega[/tex]

Thus the above approach is right.

Find out more information about resistance here:

https://brainly.com/question/76343

Explanation:

Use Pythagorean theorem:

r² = x² + y²

r² = (-7.11 m)² + (-4.41 m)²

r = 8.37 m

Use trig to find the angle.

tan θ = y / x

tan θ = (-4.41 m) / (-7.11 m)

θ = 31.8° or 211.8°

Since x is negative and y is negative, the point is in the third quadrant, so θ = 211.8°.

Or, if we subtract 360°, θ = -148.2°.

Answer:

The distance traveled by the ball is 8.5 m

Explanation:

Initial height of the ball, h₁ = 1.5 m above the ground

final height of the ball, h₂ = 5m

Upward distance = distance traveled by the ball from a height of 1.5m to 5m = 5m - 1.5m = 3.5 m

Downward distance = distance traveled by the ball from 5m height to the ground =5m - 0 = 5m

Total distance traveled = upward distance + downward distance

Total distance traveled = 3.5 m + 5m = 8.5 m

Therefore, the distance traveled by the ball is 8.5 m

Explanation:

nitrogen fixation is the process by which nitrogen gas form the atmosphere is converted into different compound that can be used by plants and animal. there are three major ways in which this happens: first, by lightning, second by industrial methods and finally by bacteria living in the soil.

Answer:

i) 60 W

ii) 100 W

Explanation:

In each case, the bulb that dissipates the most power is the bulb that glows brighter.  Power is voltage times current (P = VI).  Using Ohm's law, we can rewrite this as P = I²R or P = V²/R.

Bulbs are rated at a certain power for a certain voltage.  P = V²/R, so the bulb with the lower resistance will have the higher power rating.  Therefore, the 100 W bulb has a lower resistance than the 60 W bulb.

i) They are in series, so they have the same current.  P = I²R, so the bulb with the higher resistance will glow brighter.  That's the 60 W bulb.

ii) They are in parallel, so they have the same voltage.  P = V²/R, so the bulb with the lower resistance will glow brighter.  That's the 100 W bulb.

Answer:

The cue ball crashing into the eight balls on a pool table.

Explanation:

Elastic and inelastic collisions are two types of collisions.

For elastic collision, both the momentum and the kinetic energy before and after the collision remains conserved.

Out of the given options, the option that shows an example of an elastic collision is option A " The cue ball crashing into the eight balls on a pool table." All the eight balls after crashing moves with different velocity.

Answer:

111op

Explanation:

Answer:

11op

Explanation:good job and work hard

Answer:

12 i. The work done by Wale = 107.910 kJ

The work done by Lekan = 117.720 kJ

Total work done = 225.36 kJ

ii. Wale's power =  4.3164 kW

Lekan's power = 3.924 kW

Wale has more power and is more powerful than Lekan

13. 313.92 N

Explanation:

i. The work done, W = Force, F × Distance moved by the force, D

The given parameters are

The mass of Wale = 55 kg

The mass of Lekan = 60 kg

The acceleration due to gravity, g =9.81 m/s²

The motion force of Wale and Lekan are;

Motion force of Wale = 9.81 × 55 = 539.55 N

Motion force of Lekan = 9.81 × 60 = 588.6 N

The work done by Wale = 539.55 × 200 = 107910 J = 107.910 kJ

The work done by Lekan= 588.6 × 200 = 117720 J = 117.720 kJ

107910 + 117720 =225630 J = 225.36 kJ

ii. Power = Work done/time

Wale finished the race in 25 s, therefore, his power = 107910/25 = 4316.4 W

Lekan finished the race in 30 s, therefore, his power = 117720/30 = 3924 W

Wale has more power and is more powerful than Lekan

13. The velocity ratio = 5

V. R. = Distance moved by effort/(Distance moved by load)

Efficiency = 80%

Work done by effort = x

Work done by machine = Efficiency × Work done by effort  = 0.8 × x

Distance moved by effort, E = V. R. × Distance moved by load, D = 5 × D

Work done by effort = Force × Distance moved = 200×9.81× E

Work done by effort = 1962×E = 1962×E = 1962×5×D

Work done by machine = 1962 × D, when D = 1, we have;

0.8 × 1962×1 = 1569.6 J

Work done by effort = Force × Distance moved

Work done by effort = Force × 5×D = Force × 5 (D = 1)

From the principle of conservation of energy, we have;

Energy is neither created nor destroyed

Therefore

Work done by effort = Force × 5 = 1569.6 J

Force = 1569.6 /5 = 313.92 N.