Question

What is the mass of a large ship that has a momentum of 1.60×109kg·m/s, when the ship is moving at a speed of 48.0 km/h? (b) Compare the ship’s momentum to the momentum of a 1100-kg artillery shell fired at a speed of 1200 m/s.

Answer 1

a) The mass of the ship is $1.2\cdot 10^8 kg$

b) The ship has a larger momentum than the shell

Explanation:

a)

The momentum of an object is given by:

$p=mv$

where

m is the mass of the object

v is its velocity

For the ship in this problem, we have

$p=1.60\cdot 10^9 kg m/s$ is the momentum

$v=48.0 km/h \cdot \frac{1000 m/km}{3600 s/h}=13.3 m/s$ is the velocity

Solving for m, we find the mass of the ship:

$m=\frac{p}{v}=\frac{1.60\cdot 10^9}{13.3}=1.2\cdot 10^8 kg$

b)

The momentum of the artillery shell is given by

$p=mv$

where

m is its mass

v is its velocity

For the shell in this problem,

m = 1100 kg

v = 1200 m/s

Substituting,

$p=(1100)(1200)=1.32\cdot 10^6 kg m/s$

So, we see that the ship has a larger momentum.

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Answer 2

Momentum is the product of force and velocity. The mass of the ship and the momentum of the fired artillery is $1.2 \times 10^{8}$ and $1.32 \times 10^{6} kgm/s$ respectively

Momentum = mass × velocity

• momentum, p = $1.60 \times 10^{9}$
• Speed, v = $48 km/hr$
• Speed in m/s = (48×1000)/3600 = 13.33 m/s

Mass of the ship = momentum / velocity

Mass of ship = $\frac{1.60 \times 10^{9}}{13.33} = 1.2 \times 10^{8}$

2.)

• Speed, v = 1200 m/s
• Mass, m = 1100 kg

Momentum of fired artillery = 1100 × 1200 = $1.32 \times 10^{6} kgm/s$

Therefore, the momentum of fired artillery is $1.32 \times 10^{6} kgm/s$

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