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Suppose a 210 kg motorcycle has two 11.5 kg wheels and is heading toward a hill at a speed of 31.0 m/s. Assume each wheel to be approximately an annular ring, as shown in the figure below, with an inner radius of 0.280 m and an outer radius of 0.330 m. (a) How high (in m) can it coast up the hill, if you neglect friction? m (b) How much energy (in J) is lost to friction if the motorcycle only gains an altitude of 30.0 m before coming to rest?

Suppose a 210 kg motorcycle has two 11.5 kg wheels and is heading toward a hill at a speed of 31.0 m/s. Assume each wheel to be approximately an annular ring, as shown in the figure below, with an inner radius of 0.280 m and an outer radius of 0.330 m. (a) How high (in m) can it coast up the hill, if you neglect friction? m (b) How much energy (in J) is lost to friction if the motorcycle only gains an altitude of 30.0 m before coming to rest?

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**Transcription:** Suppose a 210 kg motorcycle has two 11.5 kg wheels and is heading toward a hill at a speed of 31.0 m/s. Assume each wheel to be approximately an annular ring, as shown in the figure below, with an inner radius of 0.280 m and an outer radius of 0.330 m. [Diagram Explanation] - The image displays the rear wheel of a motorcycle, illustrating its rotational and linear dynamics. - The wheel is depicted as an annular ring with an inner radius labeled \( r_1 = 0.280 \, \text{m} \) and an outer radius labeled \( r_2 = 0.330 \, \text{m} \). - Forces and motion are indicated: - \( \omega \) represents the angular velocity in a clockwise direction. - \( F \) (blue) represents the linear forward force. - Arrows (orange) show the rotational motion direction around the center. Questions: (a) How high (in m) can it coast up the hill, if you neglect friction? [Input box for answer] m (b) How much energy (in J) is lost to friction if the motorcycle only gains an altitude of 30.0 m before coming to rest? [Input box for answer] J
Transcribed Image Text:**Transcription:** Suppose a 210 kg motorcycle has two 11.5 kg wheels and is heading toward a hill at a speed of 31.0 m/s. Assume each wheel to be approximately an annular ring, as shown in the figure below, with an inner radius of 0.280 m and an outer radius of 0.330 m. [Diagram Explanation] - The image displays the rear wheel of a motorcycle, illustrating its rotational and linear dynamics. - The wheel is depicted as an annular ring with an inner radius labeled \( r_1 = 0.280 \, \text{m} \) and an outer radius labeled \( r_2 = 0.330 \, \text{m} \). - Forces and motion are indicated: - \( \omega \) represents the angular velocity in a clockwise direction. - \( F \) (blue) represents the linear forward force. - Arrows (orange) show the rotational motion direction around the center. Questions: (a) How high (in m) can it coast up the hill, if you neglect friction? [Input box for answer] m (b) How much energy (in J) is lost to friction if the motorcycle only gains an altitude of 30.0 m before coming to rest? [Input box for answer] J
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