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A) A 400.0-g ball of radius 4.6-cm rolls without slipping on a looped track and then launches upwards at a 30-degree angle from the horizontal off of a 1.20-m high desk. The departure point of the track is 20.0-cm above the top of the desk. The starting point is 1.40-m above the surface of the desk. The track consists of a 2.00-m initial straight section at a 45-degree angle, followed by a 70-cm diameter loop, followed by a 40-cm straight section that launches a ball. A) Prove that the ball will make it around the loop without falling off the track. B) Assuming no friction, where will the ball land? C) If the ball lands on the floor 1.50-m horizontally from the launch point, what was the average friction force acting on the ball as it rolled along the track? D) If the track was frictionless and the ball slid instead of rolled, would the ball have flown a farther or shorter distance? Explain why.

A) A 400.0-g ball of radius 4.6-cm rolls without slipping on a looped track and then launches upwards at a 30-degree angle from the horizontal off of a 1.20-m high desk. The departure point of the track is 20.0-cm above the top of the desk. The starting point is 1.40-m above the surface of the desk. The track consists of a 2.00-m initial straight section at a 45-degree angle, followed by a 70-cm diameter loop, followed by a 40-cm straight section that launches a ball. A) Prove that the ball will make it around the loop without falling off the track. B) Assuming no friction, where will the ball land? C) If the ball lands on the floor 1.50-m horizontally from the launch point, what was the average friction force acting on the ball as it rolled along the track? D) If the track was frictionless and the ball slid instead of rolled, would the ball have flown a farther or shorter distance? Explain why.

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4. A) A 400.0-g ball of radius 4.6-cm rolls without slipping on a looped track and then launches upwards at a 30-degree angle from the horizontal off of a 1.20-m high desk. The departure point of the track is 20.0-cm above the top of the desk. The starting point is 1.40-m above the surface of the desk. The track consists of a 2.00-m initial straight section at a 45-degree angle, followed by a 70-cm diameter loop, followed by a 40-cm straight section that launches a ball. A) Prove that the ball will make it around the loop without falling off the track. B) Assuming no friction, where will the ball land? C) If the ball lands on the floor 1.50-m horizontally from the launch point, what was the average friction force acting on the ball as it rolled along the track? D) If the track was frictionless and the ball slid instead of rolled, would the ball have flown a farther or shorter distance? Explain why.
Transcribed Image Text:4. A) A 400.0-g ball of radius 4.6-cm rolls without slipping on a looped track and then launches upwards at a 30-degree angle from the horizontal off of a 1.20-m high desk. The departure point of the track is 20.0-cm above the top of the desk. The starting point is 1.40-m above the surface of the desk. The track consists of a 2.00-m initial straight section at a 45-degree angle, followed by a 70-cm diameter loop, followed by a 40-cm straight section that launches a ball. A) Prove that the ball will make it around the loop without falling off the track. B) Assuming no friction, where will the ball land? C) If the ball lands on the floor 1.50-m horizontally from the launch point, what was the average friction force acting on the ball as it rolled along the track? D) If the track was frictionless and the ball slid instead of rolled, would the ball have flown a farther or shorter distance? Explain why.
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