Cart A has a mass of 5 kg and is moving in the + x direction at 2 m/s . Cart B h

Question

Cart A has a mass of 5 kg and is moving in the +x direction at 2 m/s . Cart B has a mass of 2 kg and is moving in the +y direction at 5 m/s .

Part A

Do the two carts have the same momentum? Explain.

Cannot determine from the given information.

Part B

Is the magnitude of the momentum of each cart the same? Explain.

Cannot determine from the given information.

Part C

Is the kinetic energy of each cart the same? Explain.

Yes, they both have a momentum of magnitude 10. No, they do not have the same momentum because they move in different directions.

Cannot determine from the given information.

Part B

Is the magnitude of the momentum of each cart the same? Explain.

Yes, the product of each mass and velocity gives the same momentum magnitude. No, the magnitude is different because they move in different directions.

Cannot determine from the given information.

Part C

Is the kinetic energy of each cart the same? Explain.

No, kinetic energy has a squared dependance on velocity thus, cart B has higher kinetic energy than cart A . Yes, kinetic energy is just the magnitude of the momentum vector. No, they move in different directions. Yes, kinetic energy is the same regardless of direction.

Explanation / Answer

mass of cart A is, m1=5kg,

speed of cart A is, v1=2m/sec

and

mass of the cart B is, m2=2kg

speed of the cart B is, v2=5m/sec

A)

momentum, P1=m1*v1

P1=5*2

P1=10 kg.m/sec (along x-axis)

and

P2=m2*v2

P2=2*5

P2=10 kg.m/sec (along y -axis)

both cartA and cartB have the same momentum(magnitude),

but has the different direction,

B)

P1=P2=10 kg.m/sec

the poduct of each mass and velocity gives the same momentum magnitude,

C)

K.E1=1/2*m1*V^2

=1/2*5*2^2

=10 J

and

K.E2=1/2*m2*v^2

=1/2*2*5^2

=50 J

therefore,K.E2 > K.E1

No, kinetic energy has a squared dependance on velocity thus, cart B has higher kinetic energy than cart A .

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