Weekly 07: Dynamics in Multiple Dimensions, Momentum and Impulse Item 31 31 of 3

Question

Weekly 07: Dynamics in Multiple Dimensions, Momentum and Impulse Item 31 31 of 35 First, find the magnitude of v, that is, the speed v of the two-car unit after the collision Express v in terms of m1, m2, and the cars initial speeds vi and v2 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. View Available Hint(s) Two cars of masses mi 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. (Figure 1)After the collision the two cars stick together and travel off in the direction shown u= Submit Part B Find the tangent of the angle Express your answer in terms of the momenta of the two cars, pi and p2 Figure 1 of 1 tan()- Submit Request Answer in Car 1 Part C Suppose that after the collision, tan -1, in other words, is 45°. This means that before the collision O The magnitudes of the momenta of the cars were equal. O The masses of the cars were equal O The velocities of the cars were equal Car 2

Explanation / Answer

Apply conservation of momentum allong horizontal direction

m1 v1 = m1 + m2) vx

vx = m1v1/ ( m1 + m2)

in vertical directoin

m2 v2 = (m1 + m2) vy

vy = m2v2/ ( m1 + m2)

magnitude of velocity

v = sqrt vx^2 + vy^2

= sqrt (  m1v1/ ( m1 + m2))^2 + 9 m2v2/ ( m1 + m2))^2

= sqrt ( m1 v1)^2 + ( m2 v2)^2/ m1 + m2

(b)

tan theta = p2/p1

(c)

tan 45 = p2/p1

p2 = p1

The magnitudes of the momenta of the cars were equal.

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