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4 years ago

6

During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one another with large catapu

lts that are made with surgical hose mounted on a window frame. A balloon filled with dyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room. Assume that the stretching of the hose obeys Hooke's law with a spring constant of 82.0 N/m. If the hose is stretched by 2.70 m and then released, how much work does the force from the hose do on the balloon in the pouch by the time the hose reaches its relaxed length?

1 answer:

natali 33 [55]4 years ago

4 0

Answer:

110.7 J

Explanation:

Hooke's law is represented by the formula:

F = ke where F is the force in Newton, K is force constant and e is extension in m

work done = 1/2ke² = 1/2 K ( e² - e₀²) and e₀ is the extension at relaxed length

e₀ =0

work done = 0.5 × 82N/m × (2.70 m)² = 110.7 J

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Allushta [10]

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$p_i = p_1-p_2 = mv-mv =0$
So, the final momentum must be zero as well:
$p_f = 0$
Calling v1 and v2 the velocities of the two balls after the collision, the final momentum can be written as
$p_f = mv_1 + mv_2 = 0$
From which
$v_1 = -v_2$

- So now let's apply conservation of kinetic energy. The kinetic energy of each ball is $\frac{1}{2} mv^2$ . Therefore, the total kinetic energy before the collision is
$K_i = \frac{1}{2} mv^2 + \frac{1}{2} mv^2 = mv^2$
the kinetic energy after the collision must be conserved, and therefore must be equal to this value:
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But the final kinetic energy, Kf, is also
$K_f = \frac{1}{2} mv_1^2 + \frac{1}{2}mv_2^2$
Substituting $v_1 = -v_2$ as we found in the conservation of momentum, this becomes
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we also said that Kf must be equal to the initial kinetic energy (1), therefore we can write
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Therefore, the two final speeds of the balls are
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This means that after the collision, the two balls have same velocity v, but they go in the opposite direction with respect to their original direction.

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3 years ago

When a garden hose with an output diameter of 20 mm is directed straight upward, the stream of water rises to a height of 0.13m

SpyIntel [72]

Answer: h = 0.52m

Explanation:

Using the equation of out flow;

A1 × V1 = A2 ×V2

Where A1 = area of the first nozzle

A2 = area of the second nozzle

V1= velocity of flow out from the first nozzle

V2 = velocity of flow out from 2nd nozzle

But AV= area of nozzle × velocity of water = volume of water per second(m³/s).

Now we can set A×V = Area of nozzle × height of rise.

Henceb A1× h1 = A2 × h2 ( note the time cancel on both sides)

D1 = 20mm= 0.02m; h1 = 0.13m

D2 = 10mm = 0.01m; h2= ?

h2 = π(D1/2)²× h1 /π(D2/2)²

h2 = (0.02/2)² × 0.13/(0.01/2)²

= (0.01)² ×0.13 /(0.005)²

= 1.3 × 10^-5/(5 × 10^-3)²

= 1.3 × 10^-5/25 × 10^-6

= (1.3/25) 10^-5 × 10^6

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7 0

3 years ago

1.45 L of 16°C water is placed in a refrigerator. The refrigerator's motor must supply an extra 10.7 W power to chill the water

Vika [28.1K]

Answer:

The coefficient of performance of the refrigerator is 2.251.

Explanation:

In this case, the coefficient of performance of the refrigerator ( $COP$ ), no unit, is equal to the ratio of the heat rate received from the water to the power needed to work, that is:

$COP = \frac{\dot Q_{L}}{\dot W}$ (1)

$COP = \frac{\rho\cdot V\cdot c_{w}\cdot \Delta T}{\dot W \cdot \Delta t}$ (2)

Where:

$\dot Q_{L}$ - Heat rate received from the water, in watts.

$\dot W$ - Power, in watts.

$\rho$ - Density of water, in kilograms per cubic meter.

$V$ - Volume of water, in cubic meters.

$c_{w}$ - Specific heat of water, in joules per kilogram-degree Celsius.

$\Delta T$ - Temperature change, in degrees Celsius.

$\Delta t$ - Cooling time, in seconds.

If we know that $\rho = 1000\,\frac{kg}{m^{3}}$ , $V = 1.45\times 10^{-3}\,m^{3}$ , $c_{w} = 4187\,\frac{J}{kg\cdot ^{ \circ}C}$ , $\Delta T = 10\,^{\circ}C$ , $\dot W = 10.7\,W$ and $\Delta t = 2520\,s$ , then the coefficient of refrigeration of the refrigerator is:

$COP = \frac{\rho\cdot V\cdot c_{w}\cdot \Delta T}{\dot W \cdot \Delta t}$

$COP = 2.251$

The coefficient of performance of the refrigerator is 2.251.

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3 years ago

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Bogdan [553]

A cuz the soil wi;l have the most tiny rock particularly i think feel free to ask any questions marked brailiest would be appreciated

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3 years ago

You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling a

larisa86 [58]

Answer:

120 m

Explanation:

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$T=2\pi \sqrt{\frac{L}{g} }$

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g is the gravity

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