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dedylja [7]
3 years ago
12

Two objects of the same mass move along the same line in opposite directions. The first mass is moving with speed . The objects

collide, stick together, and move with speed 0.100 in the direction of the velocity of the first mass before the collision. What was the speed of the second mass before the collision?
0.00
0.800
0.900
10.0
1.20
and show your work please
Physics
1 answer:
Alexandra [31]3 years ago
6 0

Explanation:

Let the mass of two objects be m. Both objects move along the same line in opposite directions. Let v and u₂ are speeds of both objects before collision.

After the collision, both objects stick together and move with the speed of 0.1 V the direction of the velocity of the first mass before the collision.

Using the conservation of momentum as :

m_1u_1+m_2u_2=(m_1+m_2)v

V=\dfrac{m_1u_1+m_2u_2}{(m_1+m_2)}

V=\dfrac{m(u_1+u_2)}{(m_1+m_2)}

0.1v=\dfrac{m(v+u_2)}{(2m)}

On solving above equation, u_2=-0.8v

So, the speed of the second mass before the collision is 0.8 v. The negative sign shows that the it moves in opposite direction. Hence, this is the required solution.

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A ray of light traveling through air strikes a piece of diamond at an angle of incidence equal to 56 degrees. Calculate the angu
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The angle of separation is  \Delta \theta =  0.93 ^o

Explanation:

From the question we are told that

    The angle of incidence is  \theta  _ i  = 56^o

     The refractive index of violet light  in diamond  is  n_v = 2.46

       The refractive index of red light in diamond is n_r = 2.41

      The wavelength of violet light is  \lambda _v = 400nm = 400*10^{-9}m

         The wavelength of red  light is  \lambda _r = 700nm = 700*10^{-9}m

Snell's  Law can be represented mathematically as

         \frac{sin \theta_i}{sin \theta_r} = n

Where \theta_r is the angle of refraction

=>       sin \theta_r  =   \frac{sin \theta_i}{n}

Now considering violet light

               sin \theta_r__{v}}  =   \frac{sin \theta_i}{n_v}

substituting values

                sin \theta_r__{v}}  =   \frac{sin (56)}{2.46}

                 sin \theta_r__{v}}  =  0.337

                 \theta_r__{v}}  =  sin ^{-1} (0.337)

                 \theta_r__{v}}  =  19.69^o

Now considering red light

               sin \theta_r__{R}}  =   \frac{sin \theta_i}{n_r}

substituting values

                sin \theta_r__{R}}  =   \frac{sin (56)}{2.41}

                 sin \theta_r__{R}}  =  0.344

                 \theta_r__{R}}  =  sin ^{-1} (0.344)

                 \theta_r__{R}}  = 20.12^o

The angle of separation between the red light and the violet light is mathematically evaluated as

                  \Delta \theta = \theta_r__{R}} -  \theta_r__{V}}

substituting values

                  \Delta \theta =20.12 - 19.69

                  \Delta \theta =  0.93 ^o

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