**Physics Problem: Squid Recoil and Frictional Work****Problem Statement:**(a) A 5.50 kg squid initially at rest ejects 0.250 kg of fluid with a velocity of 10.1 m/s. What is the recoil velocity (in m/s) of the squid if the ejection is done in 0.100 s, and there is a 5.20 N frictional force opposing the squid's movement? (Enter the magnitude.)\[ \text{Result: } 0.376 \, \text{m/s} \](b) How much energy (in J) is lost to work done against friction?\[ \text{Result: } 0.21 \, \text{J} \]**Explanation:**1. **Recoil Velocity Calculation (a):** - Mass of squid (\(m_1\)): 5.50 kg - Mass of ejected fluid (\(m_2\)): 0.250 kg - Velocity of ejected fluid (\(v_2\)): 10.1 m/s - Frictional force opposing movement (\(f\)): 5.20 N - Time duration of ejection (\(\Delta t\)): 0.100 s Applying the conservation of momentum principle: \[ m_1 v_1' = m_2 v_2 \] \[ v_1' = \frac{m_2 v_2}{m_1} \] Where \(v_1'\) is the recoil velocity of the squid.2. **Energy Lost to Work Against Friction (b):** - Work done against friction (\(W_f\)): \( f \times d \) Where \(d\) is the distance travelled during the recoil, which can be calculated using: \[ d = v_1' \times \Delta t \] **Calculations:**For part (a), \[v_1' = \frac{0.250 \, \text{kg} \times 10.1 \, \text{m/s}}{5.50 \, \text{kg}} \approx 0.459 \, \text{m/s}\]Since there is a frictional force acting on the squid during the

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(a) A 5.50 kg squid initially at rest ejects 0.250 kg of fluid with a velocity of 10.1 m/s. What is the recoil velocity (in m/s) of the squid if the ejection is done in 0.100 s and there is a 5.20 N frictional force opposing the squid's movement? (Enter the magnitude.) 0.376 v m/s (b) How much energy (in ) is lost to work done against friction? 0.21

(a) A 5.50 kg squid initially at rest ejects 0.250 kg of fluid with a velocity of 10.1 m/s. What is the recoil velocity (in m/s) of the squid if the ejection is done in 0.100 s and there is a 5.20 N frictional force opposing the squid's movement? (Enter the magnitude.) 0.376 v m/s (b) How much energy (in ) is lost to work done against friction? 0.21

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

**Physics Problem: Squid Recoil and Frictional Work**

**Problem Statement:**

(a) A 5.50 kg squid initially at rest ejects 0.250 kg of fluid with a velocity of 10.1 m/s. What is the recoil velocity (in m/s) of the squid if the ejection is done in 0.100 s, and there is a 5.20 N frictional force opposing the squid's movement? (Enter the magnitude.)

\[ \text{Result: } 0.376 \, \text{m/s} \]

(b) How much energy (in J) is lost to work done against friction?

\[ \text{Result: } 0.21 \, \text{J} \]

**Explanation:**

1. **Recoil Velocity Calculation (a):**
- Mass of squid (\(m_1\)): 5.50 kg
- Mass of ejected fluid (\(m_2\)): 0.250 kg
- Velocity of ejected fluid (\(v_2\)): 10.1 m/s
- Frictional force opposing movement (\(f\)): 5.20 N
- Time duration of ejection (\(\Delta t\)): 0.100 s

Applying the conservation of momentum principle:
\[
m_1 v_1' = m_2 v_2
\]
\[
v_1' = \frac{m_2 v_2}{m_1}
\]
Where \(v_1'\) is the recoil velocity of the squid.

2. **Energy Lost to Work Against Friction (b):**
- Work done against friction (\(W_f\)): \( f \times d \)
Where \(d\) is the distance travelled during the recoil, which can be calculated using:
\[
d = v_1' \times \Delta t
\]

**Calculations:**

For part (a),

\[
v_1' = \frac{0.250 \, \text{kg} \times 10.1 \, \text{m/s}}{5.50 \, \text{kg}} \approx 0.459 \, \text{m/s}
\]

Since there is a frictional force acting on the squid during the

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