Physics, 11.03.2020 03:07 shyra94

Consider a glancing collision between two identical spheres of 0.016 kg, with one of the spheres initially at rest. Initially the incoming projectile has a velocity of 1.50 m/s to the right and after the collision we observe that this sphere leaves the collision region with a velocity of 0.80 m/s at an angle of 25 to its initial direction. (Assume that the +x-axis is to the right and the +y-axis is up along the page. Angles are measured counterclockwise from the +x-axis. Do not assume this collision is elastic.)

A)Find the x-component of the velocity of the second sphere.

B)Find the y-component of the velocity of the second sphere.

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Answer from: Jharsh525

(a) The x-component of the second sphere's velocity is 0.775 m/s

(b) The y-component of the second sphere's velocity is -0.338 m/s

Explanation:

Conservation of Linear Momentum

The principle of the conservation of linear momentum states that the total momentum of a closed system of particles is conserved while no external forces act on any part of it, regardless of the interaction between the particles. The momentum is a vector, thus we must analyze both axes in the calculations.

The momentum can be computed as

$\vec p=m.\vec v$

where m is the mass of the particle, and $\vec v$ is its velocity. In a system of two particles, the total initial momentum is

$\vec p_o=m_1.\vec v_1+m_2.\vec v_2$

And the final momentum is

$\vec p_1=m_1.\vec v_1'+m_2.\vec v_2'$

Since the total momentum is conserved

$m_1.\vec v_1'+m_2.\vec v_2'=m_1.\vec v_1+m_2.\vec v_2$

According to the conditions of the problem, both masses are identical and sphere 2 is initially at rest (v2=0), thus

$m.\vec v_1'+m.\vec v_2'=m.\vec v_1$

Simplifying by m

$\vec v_1'+\vec v_2'=\vec v_1\text{ ......[1]}$

We know that the first sphere has a velocity of 1.5 m/s to the right. This means that the vertical component of v1 is 0:

$\vec v_1=$

We also know after the collision this same sphere travels at 0.8 m/s at an angle of 25°. The components of this velocity are

$\vec v_1'=$

(a) Solving the equation [1] for v2

$\vec v_2'=\vec v_1-\vec v_1'$

$\vec v_2'=-$

$\vec v_2'=$

The x-component of the second sphere's velocity is 0.775 m/s

(b) The y-component of the second sphere's velocity is -0.338 m/s

Answer from: Quest

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic = - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day

Answer from: Quest

I'll do it rn and then answer

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Consider a glancing collision between two identical spheres of 0.016 kg, with one of the spheres ini...