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 is the propulsion force exerted by the... 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 is the propulsion force exerted by the squid?
Understand the Problem
The question provides information about a squid's propulsion system and contains details about the mass of water drawn in and the ejection speed. It likely seeks to explore the physics behind this propulsion, such as force, momentum, or propulsion mechanics.
Answer
The velocity of the squid after ejecting the water is $-7.5 \, \text{m/s}$.
Answer for screen readers
The velocity of the squid after ejecting the water is $-7.5 , \text{m/s}$.
Steps to Solve
- Identify the given data
The problem states:
- Mass of the squid: $m_s = 8.0 , \text{kg}$
- Mass of the water drawn in: $m_w = 0.60 , \text{kg}$
- Ejection speed of the water: $v_w = 100 , \text{m/s}$
- Use the principle of conservation of momentum
According to the conservation of momentum, the momentum before and after the squid propels itself must be equal. The momentum can be defined as:
$$ p = mv $$
Where (p) is momentum, (m) is mass, and (v) is velocity.
Initially, the squid and the water are at rest, so the initial momentum is zero. After ejection:
- Total momentum after ejection:
$$ p_{final} = m_s v_s + m_w v_w $$
Where (v_s) is the velocity of the squid after ejection, which we are trying to find.
- Set the initial momentum equal to the final momentum
Since the initial momentum is 0, we have:
$$ 0 = m_s v_s + m_w v_w $$
Rearranging gives us:
$$ m_s v_s = -m_w v_w $$
- Solve for the velocity of the squid
Now, we can solve for (v_s):
$$ v_s = -\frac{m_w v_w}{m_s} $$
Substituting in the values:
$$ v_s = -\frac{0.60 , \text{kg} \times 100 , \text{m/s}}{8.0 , \text{kg}} $$
- Calculate the squid's velocity
Perform the calculation:
$$ v_s = -\frac{60}{8} = -7.5 , \text{m/s} $$
The negative sign indicates the direction of the squid's motion is opposite to that of the water.
The velocity of the squid after ejecting the water is $-7.5 , \text{m/s}$.
More Information
The squid's propulsion mechanism illustrates the principle of conservation of momentum, where the ejection of water results in the forward movement of the squid. The faster water is expelled, the faster the squid moves in the opposite direction.
Tips
- Forgetting to consider the direction of momentum: It's essential to note that the squid moves in the opposite direction of the water ejection.
- Confusing mass with weight: Ensure you're using mass (in kg) for momentum calculations, not weight (in Newtons).
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