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IRINA_888 [86]
3 years ago
5

vA 61.2-kg circus performer is fired from a cannon that is elevated at an angle of 57.8 ° above the horizontal. The cannon uses

strong elastic bands to propel the performer, much in the same way that a slingshot fires a stone. Setting up for this stunt involves stretching the bands by 2.76 m from their unstrained length. At the point where the performer flies free of the bands, his height above the floor is the same as that of the net into which he is shot. He takes 2.60 s to travel the horizontal distance of 20.8 m between this point and the net. Ignore friction and air resistance and determine the effective spring constant of the firing mechanism.
Physics
1 answer:
dsp733 years ago
3 0

Answer:

The effective spring constant of the firing mechanism is 1808N/m.

Explanation:

First, we can use kinematics to obtain the initial velocity of the performer. Since we know the angle at which he was launched, the horizontal distance and the time in which it's traveled, we can calculate the speed by:

v_0_x=\frac{x}{t}\\ \\v_0\cos\theta=\frac{x}{t}\\\\v_0=\frac{x}{t\cos\theta}

(This is correct because the horizontal motion has acceleration zero). Then:

v_0=\frac{20.8m}{(2.60s)\cos57.8\°}\\\\v_0=15.0m/s

Now, we can use energy to obtain the spring constant of the firing mechanism. By the conservation of mechanical energy, considering the instant in which the elastic band is at its maximum stretch as t=0, and the instant in which the performer flies free of the bands as final time, we have:

E_0=E_f\\\\U_e=K\\\\\frac{1}{2}kx^2=\frac{1}{2}mv^2\\\\\implies k=\frac{mv^2}{x^2}

Then, plugging in the given values, we obtain:

k=\frac{(61.2kg)(15.0m/s)^2}{(2.76m)^2}\\\\k=1808N/m

Finally, the effective spring constant of the firing mechanism is 1808N/m.

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As a moon follows its orbit around a planet, the maximum gravitational force exerted on the moon by the planet exceeds the minim
professor190 [17]

Answer:

rmax/rmin = √1.127

Explanation:

F = GmM / r²

As the masses can be assumed to be constant, the force between the two is proportional to the inverse of the square of the distance between them

(Fmax - Fmin) / Fmin = 0.127

           (Fmax - Fmin) = 0.127Fmin

       1/rmin² - 1/rmax² = 0.127(1/rmax²)

                      1/rmin² = 0.127(1/rmax²) + 1/rmax²

                      1/rmin² = 1.127(1/rmax²)

              rmax²/rmin² = 1.127

                 rmax/rmin = √1.127 ≈ 1.06160256...

8 0
3 years ago
A ray of light is incident on a flat surface of a block of polystyrene, with an index of refraction of 1.49, that is submerged i
Crazy boy [7]

Answer:

21.5°

Explanation:

Given,

Refractive index of water, n₁ = 1.33

Refractive index of polystyrene, n₂ = 1.49

Angle of reflection = ?

Angle of refraction = 19.1°

Using Snell's law

n₁ sin θ₁ = n₂ sin θ₂

1.33 x sin θ₁ = 1.49 x sin 19.1°

sin θ₁ = 0.366

θ₁  = 21.5°

According to law of reflection angle of incidence is equal to angle of reflection.

Angle of reflection =  21.5°

4 0
3 years ago
What is the drawback to using superconductors?
Fittoniya [83]

Answer:

Option A

The cost of keeping the semiconductor below the critical temperature is unreasonable

Explanation:

First of all, we need to understand what superconductors are. Superconductors are special materials that conduct electrical current with almost zero resistance. This means that there is little or no need for a voltage source to be connected to them. As a matter of fact, once a superconductor is connected to a power supply, one can remove the power supply and the current will still flow.

However, most superconducts can only conduct at very low temperatures up to -200 degrees Celcius. This is because, at that temperature, their atoms and molecules are relatively settled, hence they pose little or no resistance to the flow of current.

This as you can guess is extremely difficult to do, as you will need a lot of effort to cool it to that temperature and maintain it.

This makes option a the answer:

The cost of keeping the semiconductor below the critical temperature is unreasonable.

7 0
2 years ago
The derived unit for density are g/cm3.<br><br> True<br> False
anzhelika [568]
True, the measurement shown is a derived unit.
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3 years ago
A small airplane has to reach a speed if 27.8 m/s to takeoff. It can accelerate at 2.00 m/s^2. What is the minimal length of run
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Using the constant acceleration formula v^2 = u^2 + 2as, we can figure out that it would take a distance of 193.21m to reach 27.8m/s

3 0
3 years ago
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