Momentum and Kinetic Energy Consider two objects (Object 1 and Object 2) moving

Question

Momentum and Kinetic Energy 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 2m. Object moves with speed has mass m 1 v2 2v and has mass m2 m. Part A Which object has the larger magnitude of its momentum? o Object 1 has the greater magnitude of its momentum O Object 2 has the greater magnitude of its momentum o Both objects have the same magnitude of their momenta Submit Hints My Answers Give Up Review Part Part B Which object has the larger kinetic energy? o Object 1 has the greater kinetic energy o Object 2 has the greater kinetic energy o The objects have the same kinetic energy Submit Hints My Answers Give Up Review Part Provide Feedback Continue

Explanation / Answer

Given,

m1 = 2m and v1 = v

m2 = m and v2 = sqrt(2) v = 1.414 v

We know that, momentum is:

p = m v

p1 = m1 v1 = ( 2m) v = 2mv

p2 = m2 v2 = m (1.414 v) = 1.414mv

p1 > p2

Kinetic energy is given by:

KE = 1/2 m v2

KE1 = 1/2 m1 v12 =1/2 (2m) v2 = mv2

KE2 = 1/2 m2 v22 = 1/2 m [sqrt(2)v]2 = mv2

KE1 = KE2

(A)Object 1 has greater magnitude of momentum

(B)The objects have same kinetic energy.

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