1. Two football players collide head-on in midair while trying to catch a thrown football and cling together. The first player is 89 kg and has an initial velocity of 4 m/s, while the second player is 107 kg and has an initial velocity of -7 m/s. Ignore air resistance and friction. (a) For the system consisting of the two football players, the total momentum is: O Conserved O Not conserved (b) This collision is: O Elastic O Completely inelastic

College Physics
11th Edition
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Chapter1: Units, Trigonometry. And Vectors
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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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**Physics Problem Set Explanation:**

**Question (c):** What is their velocity \( v_f \) just after impact if they cling together?

\[ v_f = \text{\_\_\_\_\_\_\_\_\_} \, \text{(units)} \]

**Instructions for Parts (d) through (f):** Justify that friction could be ignored compared to the forces of collision by considering the change in momentum of the first player. Assume the collision lasts for 10 ms. Calculate the force on the first player by the second player during the collision. Consider only the system of the first player. Take into account both impulse and the force from friction.

**(d)** Calculate the magnitude of the force resulting from the change in the player's velocity during the collision:

\[ F_{\text{eff}} = \text{\_\_\_\_\_\_\_\_\_} \, \text{N} \]

**(e)** Calculate the force due to the weight of the player. Frictional forces usually follow \( F_R = \mu_k N = \mu_k mg \), a fraction of the weight (i.e., proportional to the weight). Make the approximation that the frictional force is equal to the player's weight.

\[ mg = \text{\_\_\_\_\_\_\_\_\_} \, \text{N} \]

**(f)** Compare the two forces (in this part, use \( mg \) to approximate \( F_k \)):

\[ \frac{F_{\text{eff}}}{mg} = \text{\_\_\_\_\_\_\_\_\_} \]

**Conclusion:** From (f), were we justified to ignore friction? 

---

This problem set aims to determine if friction can be ignored in the analysis of a collision. By calculating the force due to the collision and comparing it with the frictional force (approximated by the player's weight), one can assess the relative significance of friction.
Transcribed Image Text:**Physics Problem Set Explanation:** **Question (c):** What is their velocity \( v_f \) just after impact if they cling together? \[ v_f = \text{\_\_\_\_\_\_\_\_\_} \, \text{(units)} \] **Instructions for Parts (d) through (f):** Justify that friction could be ignored compared to the forces of collision by considering the change in momentum of the first player. Assume the collision lasts for 10 ms. Calculate the force on the first player by the second player during the collision. Consider only the system of the first player. Take into account both impulse and the force from friction. **(d)** Calculate the magnitude of the force resulting from the change in the player's velocity during the collision: \[ F_{\text{eff}} = \text{\_\_\_\_\_\_\_\_\_} \, \text{N} \] **(e)** Calculate the force due to the weight of the player. Frictional forces usually follow \( F_R = \mu_k N = \mu_k mg \), a fraction of the weight (i.e., proportional to the weight). Make the approximation that the frictional force is equal to the player's weight. \[ mg = \text{\_\_\_\_\_\_\_\_\_} \, \text{N} \] **(f)** Compare the two forces (in this part, use \( mg \) to approximate \( F_k \)): \[ \frac{F_{\text{eff}}}{mg} = \text{\_\_\_\_\_\_\_\_\_} \] **Conclusion:** From (f), were we justified to ignore friction? --- This problem set aims to determine if friction can be ignored in the analysis of a collision. By calculating the force due to the collision and comparing it with the frictional force (approximated by the player's weight), one can assess the relative significance of friction.
**Question 1**

Two football players collide head-on in midair while trying to catch a thrown football and *cling together*. The first player is 89 kg and has an initial velocity of 4 m/s, while the second player is 107 kg and has an initial velocity of -7 m/s.

Ignore air resistance and friction.

(a) For the system consisting of the two football players, the total momentum is:
- O Conserved
- O Not conserved

(b) This collision is:
- O Elastic
- O Completely inelastic
Transcribed Image Text:**Question 1** Two football players collide head-on in midair while trying to catch a thrown football and *cling together*. The first player is 89 kg and has an initial velocity of 4 m/s, while the second player is 107 kg and has an initial velocity of -7 m/s. Ignore air resistance and friction. (a) For the system consisting of the two football players, the total momentum is: - O Conserved - O Not conserved (b) This collision is: - O Elastic - O Completely inelastic
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