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4 years ago

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Light is travelling through air reaches quartz at an angle of incidence of 35°. The index of refraction of quartz is 1.54. At wh

at angle of refraction does the light travel into the quartz?

1 answer:

MatroZZZ [7]4 years ago

5 0

Answer:

1.54 = sin 35/sin r

sin r = 0.57/1.54 =0.37

r = sin^-1( 0.37)

=21.7°

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A 25,000-kg train car moving at 2.50 m/s collides with and connects to a train car of equal mass moving in the same direction at

dedylja [7]

Answer:

a) 1.75m/s

b) 14,062.5J

Explanation:

a) We solve this problem using linear momentum

$p=mv$

where $p$ is the momentum, $m$ is the mass, and $v$ is the velocity.

the momentum of the first train before the collision:

$p_{1}=m_{1}v_{1}$

where $m_{1}=25,000kg$ and $v_{1}=2.5m/s$

$p_{1}=(25,000kg)(2.5m/s)$

$p_{1}=62,500kgm/s$

the momentum of the second train before the collision:

$p_{2}=m_{2}v_{2}$

where $m_{2}=25,000kg$ and $v_{1}=1m/s$

$p_{2}=(25,000kg)(1m/s)$

$p_{2}=25,000kgm/s$

the total momentum before the collision is:

$p_{1}+p_{2}$

and due to the conservation of linear momentum: the amount of linear momentum before the collision must be the same after the collision.

so due to conservation:

$p_{1}+p_{2}=p_{f}$

the linear momentum of the two train system after the collision

$p_{f}=m_{f}v_{f}$

where $p_{f}$ is the final linear momentum, $m_{f}$ is the final mass of the system, if the two cars end up connected the mass is:

$m_{f}=25,000kg+25,000kg$ (the sum of the mass of the two cars)

$m_{f}=50,000kg$

and $v_{f}$ is the final speed: the speed of the connected cars.

so, going back to the conservation of momentum

$p_{1}+p_{2}=m_{f}v_{f}$

replacing all known values:

$87,500kgm/s=(50,000kg)v_{f}$

clearing for the final speed:

$v_{f}=\frac{87,500kgm/s}{50,000kg} =1.75m/s$

b) the initial kinetic energy:

$k1+k2$

which is:

$\frac{1}{2} m_{1}v_{1}^2+\frac{1}{2} m_{2}v_{2}$

replacing all known values:

$\frac{1}{2}(25,000kg)(2.5m/s)^2+\frac{1}{2}(25,000kg)(1m/s)^2\\=\frac{1}{2}(25,000kg)(6.25m^2/s^2)+\frac{1}{2}(25,000kg)(1m^2/s^2)\\=78,125J+12,500J\\=90,625J$

anf the final kinetic energy is:

$k_{f}=\frac{1}{2} m_{f}v_{f}^2\\k_{f}=\frac{1}{2} (50,000kg)(1.75m/s)^2\\k_{f}=\frac{1}{2} (50,000kg)(3.0625m^2/s^2)\\k_{f}=76,562.5J$

the difference is:

$90,625J-76,562.5J=14,062.5J$

the kinetic energy of the system decreased 14,062.5J

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3 years ago

A horizontal spring with spring constant of 9.80 N/m is attached to a block with a mass of 1.20 kg that sits on a frictionless s

Andreas93 [3]

Answer:

Explanation:

Given

at certain point displacement and velocity is 0.345 m and 0.54 m/s

Therefore Potential and Kinetic Energy associated is

$U=\frac{1}{2}kx^2$

$U=\frac{1}{2}\times 9.8\times (0.345)^2$

$U=0.583 J$

Kinetic Energy $K=\frac{1}{2}mv^2$

$k=\frac{1}{2}\times 1.2\times (0.54)^2=0.174 J$

Total Energy $T=U+K=0.583+0.174=0.757 J$

Total Energy is conserved hence at maximum displacement all energy will be Potential energy

$T=\frac{1}{2}kA^2$

where A=maximum displacement

$0.757=\frac{1}{2}\times 9.8\times A^2$

$0.1544=A^2$

$A=0.393 m$

Maximum speed occurs at equilibrium Position where Potential Energy is zero

thus $T=\frac{1}{2}mv^2$

$0.757=\frac{1}{2}\times 1.2\times v_{max}^2$

$v_{max}=1.123 m/s$

(c)When block is at 0.2 m from Equilibrium speed then its Potential Energy is

$U=\frac{1}{2}kx^2=\frac{1}{2}\times 9.8\times (0.2)^2=0.196 J$

$T=U+K$

$K=0.757-0.196=0.561 J$

$K=\frac{1}{2}mv^2$

$0.561=\frac{1}{2}\times 1.2\times v^2$

$v=0.966 m/s$

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4 years ago

In which scenario does radiation occur?

Airida [17]

Suntanning outside or in tanning booths are both examples.

7 0

3 years ago

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The cheetah is one of the fastest accelerating animals, for it can go from rest to 34.5 m/s in 3.57 s. If its mass is 112 kg, de

marysya [2.9K]

Answer: a) 18670 W b) 25 hp

Explanation:

a)

Average power,

P = W/t

W= 0.5 MVf^2 - 0.5 MVo^2

Therefore P =( (0.5 x 112 x 34.5^2 ) - (0.5 x 112 x 0 ) ) / 3.57

P = 1.87 x 10^4 W

b)

Power in units of horsepower is

P = 1.87 x 10^4 / 745.7 = 25hp

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3 years ago

An 85-kg refrigerator is located on the 70th floor of a skyscraper (4km above the ground ) what is the potential energy

Airida [17]

Potential energy can be calculated using the following rule:
potential energy = mgh where:
m is the mass = 85 kg
g is the acceleration due to gravity = 9.8 m/sec^2
h is the height = 4 km = 4000 meters

Substitute in the above equation to get the potential energy as follows:
Potential energy = 85*9.8*4000 = 3332000 joules

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3 years ago