A can of beans that has mass M is launched by a spring-powered device from level ground. The can is launched at an angle of α0 above the horizontal and is in the air for time T before it returns to the ground. Air resistance can be neglected.


A. How much work was done on the can by the launching device?
Express your answer in terms of some or all of the variables M , T , α0 and acceleration due to gravity g .

WA =

B. How much work is done on the can if it is launched at the same angle but stays in the air twice as long?
Express your answer in terms of some or all of the variables M , T , α0 and acceleration due to gravity g .
WB =

C. How does your result in part B compare to the answer to part A?
Express your answer to two significant figures.
WB/WA =

Answers

Answer 1

Hi there!

A.

Since the can was launched from ground level, we know that its trajectory forms a symmetrical, parabolic shape. In other words, the time taken for the can to reach the top is the same as the time it takes to fall down.

Thus, the time to its highest point:
[tex]T_h = \frac{T}{2}[/tex]

Now, we can determine the velocity at which the can was launched at using the following equation:
[tex]v_f = v_i + at[/tex]

In this instance, we are going to look at the VERTICAL component of the velocity, since at the top of the trajectory, the vertical velocity = 0 m/s.

Therefore:
[tex]0 = v_y + at\\\\0 = vsin\theta - g\frac{T}{2}[/tex]

***vsinθ is the vertical component of the velocity.

Solve for 'v':
[tex]vsin(\alpha_0) = g\frac{T}{2}\\\\v = \frac{gT}{2sin(\alpha_0)}[/tex]

Now, recall that:
[tex]W = \Delta KE = \frac{1}{2}m(\Delta v)^2[/tex]

Plug in the expression for velocity:
[tex]W = \frac{1}{2}M (\frac{gT}{2sin(\alpha_0)})^2\\\\\boxed{W = \frac{Mg^2T^2}{8sin^2(\alpha _0)}}[/tex]

B.

We can use the same process as above, where T' = 2T and Th = T.

[tex]v = \frac{gT}{sin(\alpha _0)} }\\\\W = \frac{1}{2}M(\frac{gT}{sin(\alpha _0)})^2\\\\\boxed{W = \frac{Mg^2T^2}{2sin^2(\alpha _0)}}[/tex]

C.

The work done in part B is 4 times greater than the work done in part A.

[tex]\boxed{\frac{W_B}{W_A} = \frac{4}{1} = 4.0}[/tex]

Answer 2

A. To find the work done on the can by the launching device, we need to calculate the change in kinetic energy of the can. When the can is launched, it has an initial kinetic energy of 0 (since it starts from rest).

1/2 * M * [(initial velocity)^2 * cos^2(α0) + (g * T)^2]

WA = 1/2 * M * [(initial velocity)^2 * cos^2(α0) + (g * T)^2]

B. If the can stays in the air twice as long, the time of flight becomes 2T. We can repeat the above steps with the new value of T to find the initial velocity: Initial vertical velocity = g * (2T)

WB [tex]= 1/2 * M * [(initial velocity)^2 * cos^2(α0) + (2gT)^2][/tex]

C. To compare the results, we can calculate the ratio of WB to WA:

WB/WA [tex]= [1/2 * M * [(initial velocity)^2 * cos^2(α0) + (2gT)^2]] / [1/2 * M * [(initial velocity)^2 * cos^2(α0) + (g * T)^2]][/tex]

Notice that the mass M and the angle α0 cancel out:

WB/WA [tex]= [((initial velocity)^2 * cos^2(α0) + (2gT)^2)] / [((initial velocity)^2 * cos^2(α0) + (g * T)^2)][/tex]

A.  At the highest point of its trajectory, the kinetic energy is again 0 (the vertical velocity component is 0). So the work done by the launching device equals the initial kinetic energy. The initial kinetic energy can be expressed as: Initial kinetic energy = [tex]1/2 * M * (initial velocity)^2[/tex]

The initial velocity can be calculated using the launch angle and the time of flight T. At the highest point, the vertical component of the velocity is 0, so we only consider the horizontal component of the velocity. Horizontal component of velocity = initial velocity * cos(α0). The time T is the time taken to reach the highest point, so we can write:

T = time taken to reach the highest point = (initial vertical velocity) / g

Initial vertical velocity = g * T

Now, the initial velocity can be written as:

initial velocity = + (Initial vertical   [tex])√[(Horizontal component of velocity)^2[/tex]                        

               =[tex]√[(initial velocity * cos(α0))^2 + (g * T)^2][/tex]

                =[tex]√[(initial velocity)^2 * cos^2(α0) + (g * T)^2][/tex]

Since the initial velocity is equal to the change in kinetic energy, we have: Initial kinetic energy :[tex]1/2 * M * [(initial velocity)^2 * cos^2(α0) + (g * T)^2] \\ WA = 1/2 * M * [(initial velocity)^2 * cos^2(α0) + (g * T)^2][/tex]

B. Initial velocity:

                     [tex]√[(initial velocity * cos(α0))^2 + (g * (2T))^2]\\ = √[(initial velocity)^2 * cos^2(α0) + (2gT)^2][/tex]

Now, the initial kinetic energy for this case is: Initial kinetic energy (new) [tex]= 1/2 * M * [(initial velocity)^2 * cos^2(α0) + (2gT)^2][/tex]

WB [tex]= 1/2 * M * [(initial velocity)^2 * cos^2(α0) + (2gT)^2][/tex]

C. This shows that the mass and angle do not affect the work done on the can; only the time of flight and the acceleration due to gravity influence it. Since we know that T is doubled in part B (2T), we can write:

WB/WA  [tex]= [((initial velocity)^2 * cos^2(α0) + (2g * 2T)^2)] / [((initial velocity)^2 * cos^2(α0) + (g * T)^2)][/tex]

WB/WA [tex]= [((initial velocity)^2 * cos^2(α0) + (4gT)^2)] / [((initial velocity)^2 * cos^2(α0) + (gT)^2)][/tex]

Now, we can see that WB is larger than WA by a factor of [tex][((initial velocity)^2 * cos^2(α0) + (4gT)^2)] / [((initial velocity)^2 * cos^2(α0) + (gT)^2)].[/tex]

The value of this factor will depend on the specific values of the initial velocity, launch angle, and time of flight, but this ratio is greater than 1, indicating that more work is done on the can when it stays in the air for twice the time.

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Answer:When trying to simplify and find the equivalent resistance you

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Explanation: hope this helps:)

An ideal gas initially is allowed to expand isothermally until its volume of 1.6 L and pressure is 5 kPa, undergoes isothermal expansion until its volume is 8 L and its pressure is 1 kPa.
1. Calculate the work done by the gas. Answer in units of kJ.
2. Find the heat added to the gas during this process. Answer in units of kJ.

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(a) The work done by the gas during the isothermal expansion is -25.6 J.

(b) The heat added to the gas during this process is 25.6 J.

Net work done by the ideal gas against the external pressure

The net work done by the ideal gas in the isothermal expansion is calculated as follows;

W(net) = ΔP x ΔV

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W(net) = -25.6 kPa.L

W(net) = -25.6 J

Head added to the gas

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Explanation:

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cart a having a mass of 150 kg initially moving to the right at a speed of 8 m/s collides with cart b with a mass of 150 kg, initially moving to the right at 6 m/s after a collision cart a continues to move to the right but with a speed of 5 m/s

a. what is the speed of cart b after collision
b. what is the total momentum of the system before and after collision

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The speed of cart b is 6m/s while the total momentum of the systmen is 4200 kg m/s

Conservation of Linear Momentum

Given Data

Mass of cart one M1  = 150kgInitial Velocity U1 = 8m/sFinal VelocityV1 = 5 m/s

Mass of cart two M2  = 150kg

Velocity U2 = 6m/s

Applying the principle of conservation of linear momentum we have

M1U1+M2U2 = M1V1+ M2V2

a. what is the speed of cart b after collision

substituting our given data we have

150*8+ 150*6 = 150*5+150*V2

1200 + 900 = 1200+ 150V2

2100 - 1200 = 150V2

900 = 150V2

Divide both sides by 150

V2 = 900/150

V2 = 6m/s

b. what is the total momentum of the system before and after collision

Total Momentum in the system is

Total momentum = Momentum before Impact+ Momentum after Impact

Total momentum = M1U1+M2U2 + M1V1+ M2V2

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Total momentum = 4200 kg m/s

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A p.d. of 6 V is applied across a 2 resistor. What current flows?

Answers

Answer: current is 3 A.

Explanation:

V = 6V

R = 2Ω

I = ?

∴ V = IR

I = V/R

I = 6V/2Ω

I = 6/2

I = 3 A ...answer...

hope that helps...

Answer:

3 amps

Explanation:

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Answer:

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A 3m plank AB of mass 20kg has a center of gravity 2m from end A and rests on supports R1 and R2 both 0,5m from either end. It also carries a 10kg block at end A. Calculate the reactions at R1 and R2

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How does microwave technology cook food?
Question 4 options:


By heating all the water molecules which changes the thermal energy of the food


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Microwaves cannot cook food.


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Answer:

By heating all the water molecules which changes the thermal energy of the food

Explanation:

If two runners are running in a 500 meter dash and runner #1 finishes in 25 seconds and runner #2 finishes in 27 seconds. What are the speeds of both runners? Which one is faster

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v1=25m/s

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and the first runner is faster

What are the speeds of both runners?

Generally, the equation for the speed  is mathematically given as

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How do I go about this?

Answers

Hi there!

(a)

Recall that:
[tex]W = F \cdot d = Fdcos\theta[/tex]

W = Work (J)
F = Force (N)
d = Displacement (m)

Since this is a dot product, we only use the component of force that is IN the direction of the displacement. We can use the horizontal component of the given force to solve for the work.

[tex]W =248(56)cos(30) = 12027.36 J[/tex]

To the nearest multiple of ten:
[tex]W_A = \boxed{12030 J}[/tex]

(b)
The object is not being displaced vertically. Since the displacement (horizontal) is perpendicular to the force of gravity (vertical), cos(90°) = 0, and there is NO work done by gravity.

Thus:
[tex]\boxed{W_g = 0 J}[/tex]

(c)
Similarly, the normal force is perpendicular to the displacement, so:
[tex]\boxed{W_N = 0 J}[/tex]

(d)

[tex]F_{f} =\mu_k N[/tex]

In this instance, the normal force is equivalent to the downward force of gravity and the vertical component of the applied force.

[tex]N = F_g + F_A sin(30)\\\\N = mg + F_A sin(30)\\\\N = 56(9.8) + 248sin(30) = 672.8 N[/tex]

Since the force of friction resists the applied force (assigned the positive direction), the work due to friction is NEGATIVE because energy is being LOST. Thus:
[tex]W_f = -\mu_k Nd\\W_f = - (0.1)(672.8)(56) = -3767.68J[/tex]

In multiples of ten:
[tex]\boxed{W_f = -3770 J}[/tex]

(e)
Simply add up the above values of work to find the net work.

[tex]W_{net} = W_A + W_f \\\\W_{net} = 12027.36 + (-3767.68) = 8259.68 J[/tex]

Nearest multiple of ten:
[tex]\boxed{W_{net} = 8260 J}}[/tex]

(f)
Similarly, we can use a summation of forces in the HORIZONTAL direction. (cosine of the applied force)
[tex]F_{net} = F_{Ax} - F_f[/tex]

[tex]W = F_{net} \cdot d = (F_{Ax} - F_f)[/tex]

[tex]W = (F_Acos(30) - \mu_k N)d\\W = (248cos(30) - 0.1(672.8)) * 56 \\\\W = 8259.68 J[/tex]

Nearest multiple of ten:
[tex]\boxed{W_{net} = 8260 J}[/tex]

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Explanation:

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Answer:

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Answer:

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6 (J)

Explanation:

Changing the thickness of the myelin sheath surrounding an axon changes its capacitance and thus the conduction speed. A myelinated nerve fiber has a conduction speed of 53 m/s . If the spacing between nodes is 1.0 mm and the resistance of segments between nodes is 26 MΩ , what is the capacitance of each segment?

Answers

For a myelinated nerve fiber has a conduction speed of 53 m/s, the capacitance of each segment is mathematically given as

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Generally, the equation for the Constant  is mathematically given as

t=RC

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t=V/d

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C=V/Rd

C=1.2*1)^-3/26*10^6*56

C=8.2*10^{-13}

In conclusion, the capacitance

C=8.2*10^{-13}F

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Answer:

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The radius of the aorta is about 1.4cm , and the blood passing through it has a speed of about 40cm/s .
Calculate the average speed of blood flow in the major arteries of the body, which have a total cross-sectional area of about 2.1cm2 .
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For the average speed of blood flow in the major arteries of the body  is mathematically given as

v2 = 117.29m/s

What is the average speed of blood flow in the major arteries of the body?

Generally, the equation for the average speed  is mathematically given as

A1 v1 = A2 v2

(pi r1^2) v1 = A2 v2

(3.14x(1.4)^2 )x 40 = (2.1) xV2

v2 = 117.29m/s

In conclusion, the average speed of blood flow

v2 = 117.29m/s

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Which standing wave has exactly three antinodes?
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B.
C.
D.

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Answer:

Explanation:

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As in all status wave styles, each node is separated through an antinode. This sample with 3 nodes and two antinodes is known as the second one harmonic and is depicted within the animation.

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What's a wave in technology?

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Answer ASAP and only if you know its correct
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Answers

The Equivalent resistance is :

[tex]\qquad \tt \dashrightarrow \: \dfrac{14}{9} \: \: ohms[/tex]

The solution is in attachment for solution ~

How to calculate Density of tetragonal unit cell by formula?

Answers

Answer:

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

The formula of Density for a random unit cell is as follows -

[tex]Density = \frac{ Z _{effective} \times M }{N _{a} \times a {}^{3} } \\ [/tex]

where ,

★ [tex]Z _{effective}[/tex] = number of atoms in a unit cell

★ M = molar mass

★ [tex] N _{a} = Avogadro's \: Number = 6 × 10^{23}[/tex]

★ a = edge length

now ,

In a tetragonal unit cell ,

the atoms are present over the corners as well as the at the body centre.

Therefore ,

[tex]Z _{effective} = contribution \: by \: the \: 8 \: corners \: + contribution \: by \: the \: body \: centre[/tex]

[tex]\implies \: (\frac{1}{8} \times 8) \: + \: 1 \\ \\ \implies \: 1 + 1 \\ \\ \implies2[/tex]

And ,

[tex]N _{a} = 6 \times 10 {}^{23} [/tex]

Substituting the values of the following in the formula of Density , we get

[tex]\bold\purple{Density = \frac{2 \times M}{6 \times 10 {}^{23} \times a {}^{3} }} \\[/tex]

hope helpful :D

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