A scientist studying an 8.0 kg squid observes that the squid draws in 0.60 kg of water and then ejects the water at a rate of 100 m/s². What are the implications for the squid's pr... A scientist studying an 8.0 kg squid observes that the squid draws in 0.60 kg of water and then ejects the water at a rate of 100 m/s². What are the implications for the squid's propulsion system?
Understand the Problem
The question is about a squid's propulsion system, specifically looking at the physics behind the movement of water and the squid's mass. It likely involves calculations related to momentum and propulsion based on the mass of the squid and the rate at which water is ejected.
Answer
The velocity of the squid is $-7.5 \, \text{m/s}$.
Answer for screen readers
The velocity of the squid is $-7.5 , \text{m/s}$.
Steps to Solve
- Identify given values
We know:
- Mass of the squid, $m_s = 8.0 , \text{kg}$
- Mass of water drawn in, $m_w = 0.60 , \text{kg}$
- Velocity of water ejected, $v_w = 100 , \text{m/s}$
- Calculate the momentum of the water ejected
The momentum ($p_w$) of the water can be calculated using the formula:
$$ p_w = m_w \times v_w $$
Substituting the known values:
$$ p_w = 0.60 , \text{kg} \times 100 , \text{m/s} $$
- Calculate the value of momentum
Now we can compute the momentum of the water:
$$ p_w = 60 , \text{kg} \cdot \text{m/s} $$
- Apply the conservation of momentum principle
According to the conservation of momentum, the total momentum before the water is ejected must equal the total momentum after the water is ejected:
$$ m_s \times v_s + p_w = 0 $$
Where $v_s$ is the velocity of the squid. Rearranging gives:
$$ v_s = - \frac{p_w}{m_s} $$
- Substitute known values and compute the squid's velocity
Now we substitute the values into the equation:
$$ v_s = - \frac{60 , \text{kg} \cdot \text{m/s}}{8.0 , \text{kg}} $$
Calculating this will give us the velocity of the squid.
- Final computation for velocity
Doing the calculation:
$$ v_s = - 7.5 , \text{m/s} $$
The negative sign indicates that the squid moves in the opposite direction to the ejected water.
The velocity of the squid is $-7.5 , \text{m/s}$.
More Information
This result indicates that the squid propels itself backward at a speed of 7.5 m/s when it ejects water at a high rate, utilizing the law of conservation of momentum effectively.
Tips
- Forgetting to apply the conservation of momentum properly.
- Miscalculating the momentum of the water or the velocity of the squid.
- Not recognizing that the negative sign indicates direction.
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