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PSYCHO15rus [73]
3 years ago
11

You’re in the Nevada dessert and your 1800 kg car suddenly runs out of gas. You are going 25 m/s downhill towards a valley in th

e road, but luckily there is a gas station at the top of the hill on the other side of the valley. You throw your manual transmission car into neutral to coast down the hill and do a little calculation to pass the stressful time. Assume all forms of friction are negligible. (At present your car is at the 10m height of hill and the gas station is 15m height of the hill)
a) How fast will your car be going when it’s at the bottom of the hill? Solve using energy methods. b) Will you be able to get to the gas station? If so, how fast will you be going? If not, how far up the hill did you make it? c) If you model the bottom of the hill as an arc of a circle with radius 5 m, draw the free-body diagram for the car at the bottom of the hill. d) What is the normal force on your car from the road at the bottom of the hill?
Physics
1 answer:
san4es73 [151]3 years ago
5 0

Answer:

Explanation:

1 )  Total mechanical energy of the car at the height of 10 m

1/2 mv² + mgh

.5 x 1800 x 25² + 1800  x 9.8 x 10 m

= 562500 + 176400

738900 J  

If v be the velocity at the bottom ,

Total energy of the car at the bottom

1/2 m v² + 0

Applying conservation of energy

1/2 mv² = 738900

.5 x 1800 v² = 738900

v = 28.65 m /s

Energy required by car to ascend height of 15 m

1800 x 9.8 x 15

= 264600 J

b )

This energy is more that total energy of the car at the top that is 738900 J

so car can easily reach gas station .

If V be the velocity at the gas point

Total energy at the gas point

1/2 m V² +  264600

Applying conservation of energy

1/2 m V² +  264600   =738900

.5 x 1800 x V² = 474300

V = 22.95 m / s

d ) If R be the normal reaction at the bottom

net force

R - mg = m v² / r

R = m ( g +  v² / r )

1800 ( 9.8 + 28.65² / 5 )

R = 313136 N

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In an elastic collision, a 300 kg bumper car collides directly from behind with a second, identical bumper car that is traveling
evablogger [386]

Answer:

If we had:

v_{1i}=5.3m/s

v_{2i}=5.9m/s

We will have:

v_{1f}=5.9m/s

v_{2f}=5.3m/s

Explanation:

In an elastic collision both linear momentum and kinetic energy are conserved, so we will have:

p_i=p_f

K_i=K_f

We will call our bumpers 1 and 2.

For the momentum equation we know that:

m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}

Since all the masses are the same (300kg), they cancel out:

v_{1i}+v_{2i}=v_{1f}+v_{2f}

For the kinetic energy equation we know that:

\frac{m_1v_{1i}^2}{2}+\frac{m_2v_{2i}^2}{2}=\frac{m_1v_{1f}^2}{2}+\frac{m_2v_{2f}^2}{2}

Since all the masses are the same (300kg), they cancel out (and also the 2 dividing):

v_{1i}^2+v_{2i}^2=v_{1f}^2+v_{2f}^2

We then must solve this system:

v_{1i}+v_{2i}=v_{1f}+v_{2f}

v_{1i}^2+v_{2i}^2=v_{1f}^2+v_{2f}^2

Which we will rewrite as:

v_{1i}-v_{1f}=v_{2f}-v_{2i}

v_{1i}^2-v_{1f}^2=v_{2f}^2-v_{2i}^2

The last of these equations can be written as:

(v_{1i}+v_{1f})(v_{1i}-v_{1f})=(v_{2f}+v_{2i})(v_{2f}-v_{2i})

But we know that v_{1i}-v_{1f}=v_{2f}-v_{2i}, so those cancel out:

v_{1i}+v_{1f}=v_{2f}+v_{2i}

So we can write:

v_{1i}-v_{1f}+v_{2i}=v_{2f}

v_{1i}+v_{1f}-v_{2i}=v_{2f}

Which means:

v_{1i}-v_{1f}+v_{2i}=v_{1i}+v_{1f}-v_{2i}

Which solving for the final velocity leaves us with:

v_{2i}+v_{2i}=+v_{1f}+v_{1f}

v_{1f}=v_{2i}

Grabbing any equation that relates both final velocities easily, for example v_{1i}-v_{1f}+v_{2i}=v_{2f}, we obtain:

v_{2f}=v_{1i}-v_{1f}+v_{2i}=v_{1i}-v_{1f}+v_{1f}=v_{1i}

So we conclude that the bumpers have just exchanged velocities (something sometimes seen in billiards for example):

v_{1f}=v_{2i}=5.9m/s

v_{2f}=v_{1i}=5.3m/s

3 0
3 years ago
Why does Newton's law of universal gravitation apply to all objects in the universe? Explain
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Because all objects attract in proportion to the product of their masses.Gravitational interactions exist between all objects with an intensity that is directly proportional to the product of their masses.
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3 years ago
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The wavelength of light changes as light goes from one medium to another, while the frequency remains the same. Is the wavelengt
Verizon [17]

Answer:

λw = 450 nm

λg = 402 nm

Explanation:

Frequency of a wave is defined as the number of vibrations coming out of the source in one second.

The frequency of a wave is the fundamental property of the source.

The relation among the wavelength, wave velocity and frequency is given by

wave velocity = frequency x wavelength

Frequency is constant while the velocity and wavelength changes.

wavelength in air, λa = 600 nm

Let the wavelength in water is λw.

speed of light in air, c = 3 x 10^8 m/s

speed of light in water = 75 % of c = 0.75 x 3 x 10^8 = 2.25 x 10^8 m/s

speed of light in plexglass = 67 % of c = 0.67 x 3 x 10^8 = 2.01 x 10^8 m/s

\frac{\lambda _{w}}{\lambda _{a}}=\frac{velocity in water}{velocity in light }

\lambda _{w}=600\times \frac{2.25\times 10^{8}}{3\times 10^{8}}

λw = 450 nm

\frac{\lambda _{g}}{\lambda _{a}}=\frac{velocity in glass}{velocity in light }

\lambda _{g}=600\times \frac{2.01\times 10^{8}}{3\times 10^{8}}

λg = 402 nm

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False, its not true so don'
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"the bank stood like a gray fortress at the corner of Yulee and St. Johns" is
GaryK [48]

Answer:personification

Explanation:

Trust me

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3 years ago
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