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In this problem we will consider the collision of two cars initially moving at right angles. We assume that after the collision the cars stick together and travel off as a single unit. The collision is therefore completely inelastic. Two cars of masses m1 and m2 collide at an intersection. Before the collision, car 1 was traveling eastward at a speed of v1, and car 2 was traveling northward at a speed of v2. After the collision, the two cars stick together and travel off in the direction.

Required:
a. Write the momentum conservation equation for the east-west components.
b. Write the momentum conservation equation for the north-south components.
c. Find the tangent of the angle.

Respuesta :

Answer:

a)     vfₓ = m₁ / (m₁ + m₂) v₁,  b)    tan θ  = m₂ / m₁ v₂ / v₁, c)

Explanation:

Momentum is a vector quantity, so the consideration must be fulfilled in all axes

a) conservation of the moment east-west direction

the system is formed by the two cases, so that the forces during the sackcloth have been internal and therefore the mummer remains

before the crash

                 p₀ = m₁ v₁

after the crash

                 [tex]p_{f}[/tex]= (m1 + m2) vfₓ

                p₀ = pf

                m₁ v₁ = (m₁ + m₂) vfₓ

              vfₓ = m₁ / (m₁ + m₂) v₁

b) conservation of the North-South axis moment

before the shock

                p₀ = m₂ v₂

after the crash

              p_{f} = ( m₁ +m₂) [tex]vf_{y}[/tex]  

             p₀ = p_{f}

            me 2 v₂ = (m₁ + m₂) vfy

       

            [tex]vf_{y}[/tex] = m₂ / (m₁ + m₂) v₂

c) the angle with which the car moves is

             tan θ = Vfy / Vfₓ

             tan θ = [m₂ / (m₁ + m₂) v] / [m₁ / (m₁ + m₂) v₁]

             tan θ  = m₂ / m₁ v₂ / v₁

onyebuchinnaji

The momentum conservation equation for the north-south components is [tex]m_1u_1 = v(m_1 + m_2)[/tex]

The momentum conservation equation for the north-south components is [tex]m_2u_2 = v(m_1 + m_2)[/tex]

The tangent of the angle is 1.

The given parameters;

  • angle between the initial velocity of the cars, θ = 90

Apply the principle of conservation of linear momentum of inelastic collision as shown below;

[tex]m_1u_1 + m_2u_2 = v(m_1 + m_2)[/tex]

The momentum conservation equation for the east-west components is written as follows;

[tex]m_1(u_1cos \ 0) + m_2(u_2 cos 90)= v(m_1 + m_2)\\\\m_1u_1 = v(m_1 + m_2)[/tex]

The momentum conservation equation for the north-south components is written as follows;

[tex]m_1(u_1sin 0) + m_2(u_2sin90) = v(m_1 + m_2)\\\\m_2u_2 = v(m_1 + m_2)[/tex]

The tangent of the angle is calculated as follows;

[tex]tan \ \theta = \frac{p_y}{p_x} = \frac{v(m_1 + m_2)}{v(m_1 + m_2)} \\\\tan \ \theta = 1\\\\\theta = tan^{-1} (1) \\\\\theta = 45\ ^0[/tex]

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