Answer:
1. Cart Y has a larger magnitude of momentum.
2. Because the mass of cart Y is larger than the mass of cart A.
Step-by-step explanation:
The following data were obtained from the question:
Mass of cart A (mₐ) = 2 Kg
Velocity of cart A (vₐ) = 4 m/s
Mass of cart Y (mᵧ) = 8 Kg
Velocity of cart Y (vᵧ) = 2 m/s
1. Determination of which of the cart has a larger magnitude of momentum.
For Cart A:
Mass (mₐ) = 2 Kg
Velocity (vₐ) = 4 m/s
Momentum of cart A (pₐ) =?
Momentum = mass × velocity
pₐ = mₐ × vₐ
pₐ = 2 × 4
pₐ = 8 Kgm/s
Thus, the momentum of cart A is 8 Kgm/s
For Cart Y:
Mass (mᵧ) = 8 Kg
Velocity (vᵧ) = 2 m/s
Momentum of cart Y (pᵧ) =?
Momentum = mass × velocity
pᵧ = mᵧ × vᵧ
pᵧ = 8 × 2
pᵧ = 16 Kgm/s
Thus the momentum of cart Y is 16 Kgm/s
SUMMARY:
The momentum of cart A is 8 Kgm/s
The momentum of cart Y is 16 Kgm/s
Therefore, cart Y has a larger magnitude of momentum.
2. Determination of the reason why cart Y has a larger magnitude of momentum.
Momentum is simply defined as the product of mass and velocity i.e
Momentum = mass × velocity
Thus, an increase in either mass or velocity will increase the momentum.
Considering the question given and the solution obtained:
Cart A:
Mass (mₐ) = 2 Kg
Velocity (vₐ) = 4 m/s
Momentum of cart A (pₐ) = 8 Kgm/s
Cart Y:
Mass (mᵧ) = 8 Kg
Velocity (vᵧ) = 2 m/s
Momentum of cart Y (pᵧ) = 16 Kgm/s
From the above data, we can see that the mass of cart Y (i.e 8 Kg) is larger than the mass of cart A (i.e 2 Kg).
Thus, we can conclude that the magnitude of the momentum of cart Y is larger than that of cart A irrespective of their velocities because the mass of cart Y is larger than the mass of cart A.