Consider two objects (object 1 and object 2) moving in the same direction on a frictionless surface. object 1 moves with speed v1 = v and has mass m1 = 2m. object 2 moves with speed v2 = √2v and has mass m2 = m. part a: which object has the larger momentum? a) object 1 has the greater momentum. b) object 2 has the greater momentum. c) both objects have the same momentum. part b: which object has the larger kinetic energy? object 1 has the greater kinetic energy. object 2 has the greater kinetic energy. the objects have the same kinetic energy.

1) A) Object 1 has the greater momentum

The magnitude of the momentum of an object is given by:

where

m is the mass of the object

v is its speed

Object 1 has a mass of and a speed of , so its momentum is

Object 2 has a mass of and a speed of , so its momentum is

So we see that , so object 1 has the greater momentum.

2) The objects have the same kinetic energy.

The kinetic energy of an object is given by

where

m is the mass of the object

v is its speed

Object 1 has a mass of and a speed of , so its kinetic energy is

Object 2 has a mass of and a speed of , so its kinetic energy is

So we see that , so the objects have same kinetic energy

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s