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aksik [14]
3 years ago
10

Consider two objects (Object 1 and Object 2) moving in the same direction on a frictionless surface. Object 1 moves with speed v

1 = 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.
Physics
1 answer:
d1i1m1o1n [39]3 years ago
5 0

1) A) Object 1 has the greater momentum

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

p=mv

where

m is the mass of the object

v is its speed

Object 1 has a mass of m_1 = 2m and a speed of v_1 = v, so its momentum is

p_1 = m_1 v_1 = (2m)(v)=2mv

Object 2 has a mass of m_2 = m and a speed of v_2 = \sqrt{2} v, so its momentum is

p_2 = m_2 v_2 = (m)(\sqrt{2} v)=\sqrt{2}mv

So we see that p_1 > p_2, so object 1 has the greater momentum.

2) The objects have the same kinetic energy.

The kinetic energy of an object is given by

K=\frac{1}{2}mv^2

where

m is the mass of the object

v is its speed

Object 1 has a mass of m_1 = 2m and a speed of v_1 = v, so its kinetic energy is

K_1 = \frac{1}{2}m_1 v_1^2 = \frac{1}{2}(2m)(v)^2=mv^2

Object 2 has a mass of m_2 = m and a speed of v_2 = \sqrt{2} v, so its kinetic energy is

K_2 = \frac{1}{2}m_2 v_2^2 = \frac{1}{2}(m)(\sqrt{2} v)^2=mv^2

So we see that K_1 =K_2, so the objects have same kinetic energy

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