Physics 03-09 Collisions of Point Masses in Two Dimensions
Name: _________________
Collisions in Two Dimensions
Done the ______________________ as in ______________________ dimension
Do one equation for ______________________ and one for ______________________
A 2-kg cue ball is moving at 5.00 m/s and collides with a stationary 8 ball of equal mass. After the collision the cue ball moves
at 30° to the left of the original direction and the 8-ball moves 90° to the right of the cue balls final direction. Find the
velocities after the collision.
A 1000 kg car is moving eastward at 20 m/s. It collides completely inelastically with a 1500 kg van traveling northward at 30
m/s. What is the velocity of the two vehicles immediately after the collision?
Velocity of Center of Mass
Center of mass - the ______________________ location of all the ______________________ of a ______________________
𝑚1 𝑣1 + 𝑚2 𝑣2
𝑣𝑐𝑚 =
𝑚1 + 𝑚2
The numerator is the ______________________ momentum
 Since momentum ______________________ change, the 𝑣𝑐𝑚 ______________________ change
The center of mass will travel in a ____________________________________________ at a ____________________________________________
Physics 03-09 Collisions of Point Masses in Two Dimensions
Name: _________________
Homework
1.
Where would you expect the center of mass of a doughnut to be located? Why?
2.
A sunbather is lying on a floating raft that is stationary. She then gets up and walks to one end of the raft. Consider the
sunbather and raft as an isolated system. (a) What is the velocity of the center of mass of this system while she is walking?
Why? (b) Does the raft itself move while she is walking? If so, what is the direction of the raft's velocity relative to that of
the sunbather? Provide a reason for your answer.
3.
The drawing shows a collision between two pucks on an air-hockey table. Puck A has a
mass of 0.025 kg and is moving along the x axis with a velocity of +5.5 m/s. It makes a
collision with puck B, which has a mass of 0.050 kg and is initially at rest. The collision is
not head-on. After the collision the two pucks fly apart with the angles shown in the
drawing. Find the final speed of (a) puck A and (b) puck B. (Cutnell 7.30) 3.4 m/s, 2.6 m/s
get picture
4.
Two identical pucks collide on an air hockey table. One puck was originally at rest. If the
incoming puck has a speed of 6.00 m/s and scatters to an angle of 30.0°, what is the
velocity (magnitude and direction) of the second puck if it scatters at 60°? (OpenStax 8.45)
3.00 m/s
5.
A 5.50-kg bowling ball moving at 9.00 m/s collides with a 0.850-kg bowling pin, which is
scattered at an angle of 85.0° to the initial direction of the bowling ball and with a speed of
15.0 m/s. (a) Calculate the final velocity (magnitude and direction) of the bowling ball. (b)
Is the collision elastic? (OpenStax 8.48) 9.10 m/s, No
6.
Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1200 kg and is approaching
at 8.00 m/s due south. The second car has a mass of 850 kg and is approaching at 17.0 m/s due west. (a) Calculate the final
velocity (magnitude and direction) of the cars. (b) How much kinetic energy is lost in the collision? (This energy goes into
deformation of the cars.) (OpenStax 8.50) 8.46 m/s at 33.6°, 𝟖. 𝟕𝟖 × 𝟏𝟎𝟒 J
7.
A freight train is being assembled in a switching yard. Car 1 has a mass of 𝑚1 = 65 × 103 kg and moves at a velocity of
𝑣01 = +0.80 m/s. Car 2, with a mass of 𝑚2 = 92 × 103 kg and a velocity of 𝑣02 = +1.3 m/s, overtakes car 1 and couples to
it with a common velocity of +1.1 m/s. Determine the velocity of their center of mass (a) before and (b) after the collision.
(c) Should your answer in part (b) be less than, greater than, or equal to the common velocity 𝑣𝑓 of the two coupled cars
after the collision? (Cutnell 7.42) 1.0 m/s, 1.0 m/s, same