An estimated force-time curve for a baseball struck by a bat is shown in the figure below. Let Fmay = 19,000 N, t, = 1.5 ms, and t, = 3 ms. From this curve, determine the following. LÀ. F (N) Fmax t (ms) ta (a) the magnitude of the impulse delivered to the ball N.s (b) the average force exerted on the ball kN

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**Force-Time Curve Analysis for a Baseball Hit**

An estimated force-time curve for a baseball struck by a bat is shown in the figure below. The parameters are as follows: \( F_{\text{max}} = 19{,}000 \, \text{N} \), \( t_a = 1.5 \, \text{ms} \), and \( t_b = 3 \, \text{ms} \). Based on this curve, determine the following:

![Force-Time Curve](force-time-curve.png)

### Graph Description:
- **Axes:** The x-axis represents time in milliseconds (ms), and the y-axis represents force in Newtons (N).
- **Curve Shape:** The graph shows a triangular shape with a peak at \( F_{\text{max}} \).
- **Limits:** The curve extends from time \( t = 0 \) to \( t = t_b \).
- **Peak Force:** The peak force \( F_{\text{max}} = 19{,}000 \, \text{N} \) occurs at midpoint.
- **Time Intervals:** 
  - \( t_a = 1.5 \, \text{ms} \)
  - \( t_b = 3 \, \text{ms} \)

### Calculations to Determine:
(a) **The magnitude of the impulse delivered to the ball:**
- Impulse can be determined by calculating the area under the force-time curve.
- Enter the impulse in \( \text{N} \cdot \text{s} \).

(b) **The average force exerted on the ball:**
- Calculate the average force over the duration of the contact.
- Enter the force in kN (kilonewtons).

[Input fields for student calculations]
- Impulse: [________] \( \text{N} \cdot \text{s} \)
- Average Force: [________] kN
Transcribed Image Text:**Force-Time Curve Analysis for a Baseball Hit** An estimated force-time curve for a baseball struck by a bat is shown in the figure below. The parameters are as follows: \( F_{\text{max}} = 19{,}000 \, \text{N} \), \( t_a = 1.5 \, \text{ms} \), and \( t_b = 3 \, \text{ms} \). Based on this curve, determine the following: ![Force-Time Curve](force-time-curve.png) ### Graph Description: - **Axes:** The x-axis represents time in milliseconds (ms), and the y-axis represents force in Newtons (N). - **Curve Shape:** The graph shows a triangular shape with a peak at \( F_{\text{max}} \). - **Limits:** The curve extends from time \( t = 0 \) to \( t = t_b \). - **Peak Force:** The peak force \( F_{\text{max}} = 19{,}000 \, \text{N} \) occurs at midpoint. - **Time Intervals:** - \( t_a = 1.5 \, \text{ms} \) - \( t_b = 3 \, \text{ms} \) ### Calculations to Determine: (a) **The magnitude of the impulse delivered to the ball:** - Impulse can be determined by calculating the area under the force-time curve. - Enter the impulse in \( \text{N} \cdot \text{s} \). (b) **The average force exerted on the ball:** - Calculate the average force over the duration of the contact. - Enter the force in kN (kilonewtons). [Input fields for student calculations] - Impulse: [________] \( \text{N} \cdot \text{s} \) - Average Force: [________] kN
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