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VladimirAG [237]
1 year ago
10

A projectile of mass m1 moving with speed v1 in the +x direction strikes a stationary target of mass m2 head-on. The collision i

s elastic. Use the Momentum Principle and the Energy Principle to determine the final velocities of the projectile and target, making no approximations concerning the masses. (Use the following as necessary: m1, m2, and v1.)
Physics
1 answer:
BigorU [14]1 year ago
5 0

Answer:

v''=\frac{2m_{1}v_{1}}{m_{1}+m_{2}}

v' = \frac{m_{1}-m_{2}}{m_{1}+m_{2}}v_{1}

Explanation:

first mass, m1

second mass, m2

initial velocity of m1 is v1.

initial velocity of m2 is zero.

Let the final velocity of m1 is v' and the final velocity of m2 is v''.

Collision is elastic so the coefficient of restitution is 1.

By using the conservation of momentum

m1 x v1 + m2 x 0 = m1 x v + m2 x v''

m1 v1 = m1 v' + m2 v'' .... (1)

by the formula of coefficient of restitution

1=\frac{v''-v'}{v_{1}-0}

v1 = v'' - v' .... (2)

So, v' = v'' - v1 put in equation (1)

m1 v1 = m1 x (v'' - v1) + m2 v''

m1 v1 = m1 v'' - m1 v1 + m2 v''

2 m1 v1 = (m1 + m2) v''

v''=\frac{2m_{1}v_{1}}{m_{1}+m_{2}}

so,

v' = \frac{2m_{1}v_{1}}{m_{1}+m_{2}}-v_{1}

v' = \frac{m_{1}-m_{2}}{m_{1}+m_{2}}v_{1}

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A sphere of radius 5.00 cm carries charge 3.00 nC. Calculate the electric-field magnitude at a distance 4.00 cm from the center
OlgaM077 [116]

Answer:

a)   E = 8.63 10³ N /C,  E = 7.49 10³ N/C

b)   E= 0 N/C,  E = 7.49 10³ N/C  

Explanation:

a)  For this exercise we can use Gauss's law

         Ф = ∫ E. dA = q_{int} /ε₀

We must take a Gaussian surface in a spherical shape. In this way the line of the electric field and the radi of the sphere are parallel by which the scalar product is reduced to the algebraic product

The area of ​​a sphere is

        A = 4π r²

 

if we use the concept of density

        ρ = q_{int} / V

        q_{int} = ρ V

the volume of the sphere is

      V = 4/3 π r³

         

we substitute

         E 4π r² = ρ (4/3 π r³) /ε₀

         E = ρ r / 3ε₀

the density is

         ρ = Q / V

         V = 4/3 π a³

         E = Q 3 / (4π a³) r / 3ε₀

         k = 1 / 4π ε₀

         E = k Q r / a³

 

let's calculate

for r = 4.00cm = 0.04m

        E = 8.99 10⁹ 3.00 10⁻⁹ 0.04 / 0.05³

        E = 8.63 10³ N / c

for r = 6.00 cm

in this case the gaussine surface is outside the sphere, so all the charge is inside

         E (4π r²) = Q /ε₀

         E = k q / r²

let's calculate

         E = 8.99 10⁹ 3 10⁻⁹ / 0.06²

          E = 7.49 10³ N/C

b) We repeat in calculation for a conducting sphere.

For r = 4 cm

In this case, all the charge eta on the surface of the sphere, due to the mutual repulsion between the mobile charges, so since there is no charge inside the Gaussian surface, therefore the field is zero.

         E = 0

In the case of r = 0.06 m, in this case, all the load is inside the Gaussian surface, therefore the field is

        E = k q / r²

      E = 7.49 10³ N / C

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irga5000 [103]
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1 year ago
Suppose that an asteroid traveling straight toward the center of the earth were to collide with our planet at the equator and bu
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Complete Question:

Suppose that an asteroid traveling straight toward the center of the earth were to collide with our planet at the equator and bury itself just below the surface. What would have to be the mass of this asteroid, in terms of the earth’s mass M, for the day to become 25.0% longer than it presently is as a result of the collision? Assume that the asteroid is very small compared to the earth and that the earth is uniform throughout.

Answer:

m = 0.001 M

For the whole process check the following page: https://www.slader.com/discussion/question/suppose-that-an-asteroid-traveling-straight-toward-the-center-of-the-earth-were-to-collide-with-our/

6 0
1 year ago
A 1 200-kg car traveling initially at vCi 5 25.0 m/s in an easterly direction crashes into the back of a 9 000-kg truck moving i
sukhopar [10]

Answer:

The velocity of the truck after the collision is 20.93 m/s

Explanation:

It is given that,

Mass of car, m₁ = 1200 kg

Initial velocity of the car, v_{Ci}=25\ m/s

Mass of truck, m₂ = 9000 kg

Initial velocity of the truck, v_{Ti}=20\ m/s

After the collision, velocity of the car, v_{Cf}=18\ m/s

Let v is the velocity of the truck immediately after the collision. The momentum of the system remains conversed.

initial\ momentum=final\ momentum

1200\ kg\times 25\ m/s+9000\ kg\times 20\ m/s=1200\ kg\times 18+9000\ kg\times v

210000-21600=9000\ kg\times v

v=20.93\ m/s

So, the velocity of the truck after the collision is 20.93 m/s. Hence, this is the required solution.

8 0
1 year ago
You need to determine the density of an unknown liquid and decide to perform an experiment. You notice that a wooden block float
Allushta [10]

Answer:

pu = 1260.9kg/m^3

the density of the unknown liquid is 1260.9kg/m^3

Explanation:

The density of a liquid is inversely proportional to the volume (height) of object submerged in it.

High density liquid possess higher buoyant force preventing objects from submerging.

p ∝ 1/V ∝ 1/h

since V = Ah

pu/pw = hw/hu

pu = pwhw/hu

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h = height submerged

pu and pw is the density of unknown liquid and water respectively

hu and hw is the height of object submerged in unknown liquid and water respectively

pw = 1000kg/m^3

hu = 4.6cm = 0.046m

hw = 5.8cm = 0.058m

Substituting the given values;

pu = 1000×0.058/0.046

pu = 1260.9kg/m^3

the density of the unknown liquid is 1260.9kg/m^3

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