**Physics Problem: Rotational Motion and Torque****Scenario:**You are attending a county fair with your friend from your physics class. While exploring the fairgrounds, you discover a new game requiring physics skills. A thin rod of mass \( M = 0.570 \, \text{kg} \) and length \( \ell = 2.70 \, \text{m} \) hangs from a friction-free pivot at its upper end.**Diagram Explanation:**The diagram depicts a vertical rod attached to a pivot at the top. The rod is covered with Velcro on its front surface. An incoming Velcro-covered ball of mass \( m = 1.05 \, \text{kg} \) is aimed at the rod.**Objective:**The task is to throw the ball at the rod with the aim of making it swing backward and rotate 180° over the top. If the ball sticks to the rod after striking it and causes the rod to rotate over the top, you win a stuffed animal.**Calculation:**Your friend believes striking the rod at its lowest point will apply the most torque. You must calculate the minimum speed at which the ball must be thrown to ensure the rod completes a full swing. Enter the minimum speed in meters per second (\( \text{m/s} \)) required to win the stuffed animal.**Input Box:**\[ \boxed{ \quad \text{m/s} \quad } \]

Mass of thin rod M = 0.570 kg Length of thin rod L = 2.70 m. mass of Velcro covered ball m = 1.05…

skill. A thin rod of mass M = 0.570 kg and length = 2.70 m hangs from a friction-free pivot at its upper end as shown in the figure. Pivot Velcro. Incoming Velcro-covered ball M l m The front surface of the rod is covered with Velcro. You are to throw a Velcro-covered ball of mass m = 1.05 kg at the rod in an attempt to make it swing backward and rotate all the way across the top. The ball must stick to the rod at all times after striking it. If you cause the rod to rotate over the top position (that is, rotate 180° opposite of its starting position), you win a stuffed animal. Your friend volunteers to try his luck. He feels that the most torque would be applied to the rod by striking it at its lowest end. While he prepares to aim at the lowest point on the rod, you calculate how fast he must throw the ball to win the stuffed animal with this technique. How fast must he throw the ball to win the stuffed animal? (Enter the minimum speed necessary to win in m/s.) m/s

skill. A thin rod of mass M = 0.570 kg and length = 2.70 m hangs from a friction-free pivot at its upper end as shown in the figure. Pivot Velcro. Incoming Velcro-covered ball M l m The front surface of the rod is covered with Velcro. You are to throw a Velcro-covered ball of mass m = 1.05 kg at the rod in an attempt to make it swing backward and rotate all the way across the top. The ball must stick to the rod at all times after striking it. If you cause the rod to rotate over the top position (that is, rotate 180° opposite of its starting position), you win a stuffed animal. Your friend volunteers to try his luck. He feels that the most torque would be applied to the rod by striking it at its lowest end. While he prepares to aim at the lowest point on the rod, you calculate how fast he must throw the ball to win the stuffed animal with this technique. How fast must he throw the ball to win the stuffed animal? (Enter the minimum speed necessary to win in m/s.) m/s

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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Concept explainers

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

**Physics Problem: Rotational Motion and Torque**

**Scenario:**
You are attending a county fair with your friend from your physics class. While exploring the fairgrounds, you discover a new game requiring physics skills. A thin rod of mass \( M = 0.570 \, \text{kg} \) and length \( \ell = 2.70 \, \text{m} \) hangs from a friction-free pivot at its upper end.

**Diagram Explanation:**
The diagram depicts a vertical rod attached to a pivot at the top. The rod is covered with Velcro on its front surface. An incoming Velcro-covered ball of mass \( m = 1.05 \, \text{kg} \) is aimed at the rod.

**Objective:**
The task is to throw the ball at the rod with the aim of making it swing backward and rotate 180° over the top. If the ball sticks to the rod after striking it and causes the rod to rotate over the top, you win a stuffed animal.

**Calculation:**
Your friend believes striking the rod at its lowest point will apply the most torque. You must calculate the minimum speed at which the ball must be thrown to ensure the rod completes a full swing. Enter the minimum speed in meters per second (\( \text{m/s} \)) required to win the stuffed animal.

**Input Box:**
\[ \boxed{ \quad \text{m/s} \quad } \]

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