Two carts on an air track move towards each other with velocities v 1i and v 2i
ID: 1292529 • Letter: T
Question
Two carts on an air track move towards each other with velocities v1i and v2i . The carts collide and their velocities v1f and v2f are recorded. The table provides data about the collisions including the initial velocities of the carts before the collisions, the final velocities after the collision, and the masses of the carts:
Before collision
After collision
Cart 1
Cart 2
Cart 1
Cart 2
m1(kg)
v1i (m/s)
m2(kg)
v2i (m/s)
m1(kg)
v1i (m/s)
m2(kg)
v2i (m/s)
0.1
+2.0
0.1
0
0.1
+1.0
0.1
+1.0
0.1
+2.0
0.1
-2.0
0.1
-1.0
0.1
+1.0
0.1
+2.0
0.3
-2.0
0.1
-4.0
0.3
0.0
Determine if the momentum conserves in these collisions. Does the kinetic energy conserve?
Before collision
After collision
Cart 1
Cart 2
Cart 1
Cart 2
m1(kg)
v1i (m/s)
m2(kg)
v2i (m/s)
m1(kg)
v1i (m/s)
m2(kg)
v2i (m/s)
0.1
+2.0
0.1
0
0.1
+1.0
0.1
+1.0
0.1
+2.0
0.1
-2.0
0.1
-1.0
0.1
+1.0
0.1
+2.0
0.3
-2.0
0.1
-4.0
0.3
0.0
Explanation / Answer
In all the cases, momentum conserves but the kinetic energy doesn't .
for Momentum conservation : m1v1i + m2v2i = m1v1f+m2v2f which is satisfied in all cases
for Kinetic energy conservation : m1v1i2 + m2v2i 2 = m1v1f2 +m2v2f2 which is not satisfied in any of the case
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