5.2.3 Collisions in Two Dimensions

Question 1

Collisions in Two Dimensions

Answer 1

• For collisions in two dimensions, the final velocity vector of the bodies after impact can be broken down into their x and y components.
• For elastic collisions in two dimensions, simply knowing the initial velocity vectors of the bodies is not sufficient to predict the final velocity vectors; one more piece of information is required.
• For inelastic collisions in two dimensions, knowing the initial velocity vectors of the bodies is enough to predict the final velocity vector of the resultant combined body.

Question 2

Two identical billiard balls with mass 0.4 kg are moving to the right. One ball is moving with a speed of 0.3 m/s, while the second ball is chasing it at a speed of 0.5 m/s. When they collide, the lead ball travels at an angle of 20 degrees below the horizontal. Which of the following are the speeds of the lead ball (v1) and the second ball (v2) after the collision?

Answer 2

v1 = 0.52 m/s
v2 = 0.36 m/s

Question 3

True or false?
Two pieces of clay are thrown into the air and follow parabolic paths. They collide and stick together at the highest points of their path. Just before the collision, one piece has a mass of 0.5 kg and a velocity of 4 m / s, going from left to right. The other piece has a mass of 0.4 kg and a velocity of 5 m / s, going from right to left. Just after the collision, the combined mass moves from right to left and follows a different parabolic trajectory.

Answer 3

false

Question 4

Two cars collide inelastically at an intersection. The two cars have identical masses, m, but one is driving twice as fast as the other. The incident angle is 90°. Which of the following is the velocity of the combined cars after the collision?

Answer 4

vf = 1.1vi; theta = 63 degrees

Question 5

Two electrons move toward each other along a straight line. They both have the same speed and collide elastically. After the collision, electron 1 moves at an angle of 45° relative to the horizontal with the same speed as it had before the collision. Which of the following diagrams best represents the movement of Electron 2 after the collision?

Answer 5

-

Question 6

Two identical billiard balls of mass 0.4 kg are on a table. One ball is struck with a cue and travels at 1.0 m/s toward the other, which is at rest. The balls hit slightly off-center then travel at different angles with different speeds. The ball that was struck initially travels at a 30 degree angle at a speed vi, and the second ball travels at a 45 degree angle at a speed vs. Which of the following are v1 and v2?

Answer 6

v1 = 0.73 m/s
v2 = 0.52 m/s

Question 7

Which of the following sets of equations correctly describes the inelastic collision shown in the diagram?

Answer 7

m1v1i = (m1 + m2)vf (cos theta)
m2v2i = (m1 + m2)vf (sin theta)
Ki /= Kf

Question 8

Three balls of equal mass collide together inelastically and simultaneously as shown in the diagram. Which of the following is the correct speed and angle (with respect to the horizontal) the resulting object moves after the collision?

Answer 8

vf = 0.09 m/s, theta = -90 degrees

Question 9

A model rocket is shot straight up in the air, and at its highest point explodes into two unequal pieces. The smaller piece, of mass 5 kg, moves straight down after the explosion at an initial speed of 20 m / s. How much higher does the larger piece, of mass 10 kg, travel? Assume the acceleration of gravity is 10 m / s2.

Answer 9

5 m

Question 10

Two objects collide head-on. Both objects break up into two pieces upon impact, and the four pieces move apart as shown in the diagram. Using the information from the diagram, the speed and angle of Piece 4 are more than 6 m / s and 77°, respectively. This collision is not an elastic collision.

Answer 10

true