Two cucumbers collide elastically in two dimensions. Initially, cucumber 1 moves

Question

Two cucumbers collide elastically in two dimensions. Initially, cucumber 1 moves to the right (+x) at 10 m/s and cucumber 2 is stationary. In the center of mass reference frame, the collision deflects each by an angle of 30 degree from its line of travel the cucumber have the same mass of 1 kg.

A) what is the center of mass velocity?

B) in the center of mass reference frame, what are the x and y components of the velocity of each cucumber after the collision?

C)  what are the x and y components of the velocity of each cucumber after the collision?
D) what are the deflection angles of the cucumbers? Check that the sum of the absolute values of the angles is 90 degrees. Angle 1 and angle 2?

Explanation / Answer

a)

Vcm = (m1 v1i + m2 v2i )/(m1 + m2) = (1 x 10 + 1 x 0)/(1 + 1) = 5 m/s

b)

using conservation of momentum along Y-direction

0 = m1 v1fy -  m2 v2fy

v1fy = v2fy since m1 = m2

v1f Sin30 =  v2f Sin30

v1f =  v2f

using conservation of momentum along X-direction

m1 v1i + m2 v2i = m1 v1f + m2 v2f

10 + 0 = v1f + v2f

2 v1f = 10

v1f = 5 m/s

v2f = 5 m/s

X-components :

v1fx = v2fx = 5 Cos30 = 4.33

Y-components

v1fx = v2fx = 5 Sin30 = 2.5

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.