Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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The amount of work, W, required to move a particle of mass M a vertical distance d above its starting height is given by the formula: W = Mgd where g is the acceleration due to gravity. A heavy rope is 15 m long and has a constant (linear) density of p = 2 kg/m. The rope hangs over the edge of a 25 m building, as shown below: 25 BUILDING Ay = M₂ = y3 = 25 Y₂ = Y₁ The work required to pull the rope to the top of the building cannot be computed using the above formula because the distance each part of the rope must be moved is different! Answer the following questions and put your final answer for each part in the box. I. (The Approximate Work) A. On the figure above, the rope has been divided into three segments of equal length, Ay. Calculate Ay. d₂ = Yo ROPE B. Find the mass, M₂, of the middle segment of the rope. W₂ = y=0 C. The y values of the bottom of each segment of rope are indicated above. Find the values yo, y₁, and y2 and label them on the figure (No justification is necessary). By approximating that the middle segment is a particle located at y2: D. Find the distance d2 the middle segment must be moved to reach the top of the building. E. Find the approximate the work, W₂ required to move the middle segment to the top of the building by using the given formula. For computational convenience, take g = 10 m/s².
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Transcribed Image Text:The amount of work, W, required to move a particle of mass M a vertical distance d above its starting height is given by the formula: W = Mgd where g is the acceleration due to gravity. A heavy rope is 15 m long and has a constant (linear) density of p = 2 kg/m. The rope hangs over the edge of a 25 m building, as shown below: 25 BUILDING Ay = M₂ = y3 = 25 Y₂ = Y₁ The work required to pull the rope to the top of the building cannot be computed using the above formula because the distance each part of the rope must be moved is different! Answer the following questions and put your final answer for each part in the box. I. (The Approximate Work) A. On the figure above, the rope has been divided into three segments of equal length, Ay. Calculate Ay. d₂ = Yo ROPE B. Find the mass, M₂, of the middle segment of the rope. W₂ = y=0 C. The y values of the bottom of each segment of rope are indicated above. Find the values yo, y₁, and y2 and label them on the figure (No justification is necessary). By approximating that the middle segment is a particle located at y2: D. Find the distance d2 the middle segment must be moved to reach the top of the building. E. Find the approximate the work, W₂ required to move the middle segment to the top of the building by using the given formula. For computational convenience, take g = 10 m/s².
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Please only answer D and E with work shown please, thank you.

The amount of work, W, required to move a particle of mass M a vertical distance d above its starting height is given by the formula: W = Mgd where g is the acceleration due to gravity. A heavy rope is 15 m long and has a constant (linear) density of p = 2 kg/m. The rope hangs over the edge of a 25 m building, as shown below: 25 BUILDING Ay = M₂ = y3 = 25 Y₂ = Y₁ The work required to pull the rope to the top of the building cannot be computed using the above formula because the distance each part of the rope must be moved is different! Answer the following questions and put your final answer for each part in the box. I. (The Approximate Work) A. On the figure above, the rope has been divided into three segments of equal length, Ay. Calculate Ay. d₂ = Yo ROPE B. Find the mass, M₂, of the middle segment of the rope. W₂ = y=0 C. The y values of the bottom of each segment of rope are indicated above. Find the values yo, y₁, and y2 and label them on the figure (No justification is necessary). By approximating that the middle segment is a particle located at y2: D. Find the distance d2 the middle segment must be moved to reach the top of the building. E. Find the approximate the work, W₂ required to move the middle segment to the top of the building by using the given formula. For computational convenience, take g = 10 m/s².
expand button
Transcribed Image Text:The amount of work, W, required to move a particle of mass M a vertical distance d above its starting height is given by the formula: W = Mgd where g is the acceleration due to gravity. A heavy rope is 15 m long and has a constant (linear) density of p = 2 kg/m. The rope hangs over the edge of a 25 m building, as shown below: 25 BUILDING Ay = M₂ = y3 = 25 Y₂ = Y₁ The work required to pull the rope to the top of the building cannot be computed using the above formula because the distance each part of the rope must be moved is different! Answer the following questions and put your final answer for each part in the box. I. (The Approximate Work) A. On the figure above, the rope has been divided into three segments of equal length, Ay. Calculate Ay. d₂ = Yo ROPE B. Find the mass, M₂, of the middle segment of the rope. W₂ = y=0 C. The y values of the bottom of each segment of rope are indicated above. Find the values yo, y₁, and y2 and label them on the figure (No justification is necessary). By approximating that the middle segment is a particle located at y2: D. Find the distance d2 the middle segment must be moved to reach the top of the building. E. Find the approximate the work, W₂ required to move the middle segment to the top of the building by using the given formula. For computational convenience, take g = 10 m/s².
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Follow-up Questions
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Follow-up Question

Please only answer D and E with work shown please, thank you.

The amount of work, W, required to move a particle of mass M a vertical distance d above its starting height is given by the formula: W = Mgd where g is the acceleration due to gravity. A heavy rope is 15 m long and has a constant (linear) density of p = 2 kg/m. The rope hangs over the edge of a 25 m building, as shown below: 25 BUILDING Ay = M₂ = y3 = 25 Y₂ = Y₁ The work required to pull the rope to the top of the building cannot be computed using the above formula because the distance each part of the rope must be moved is different! Answer the following questions and put your final answer for each part in the box. I. (The Approximate Work) A. On the figure above, the rope has been divided into three segments of equal length, Ay. Calculate Ay. d₂ = Yo ROPE B. Find the mass, M₂, of the middle segment of the rope. W₂ = y=0 C. The y values of the bottom of each segment of rope are indicated above. Find the values yo, y₁, and y2 and label them on the figure (No justification is necessary). By approximating that the middle segment is a particle located at y2: D. Find the distance d2 the middle segment must be moved to reach the top of the building. E. Find the approximate the work, W₂ required to move the middle segment to the top of the building by using the given formula. For computational convenience, take g = 10 m/s².
expand button
Transcribed Image Text:The amount of work, W, required to move a particle of mass M a vertical distance d above its starting height is given by the formula: W = Mgd where g is the acceleration due to gravity. A heavy rope is 15 m long and has a constant (linear) density of p = 2 kg/m. The rope hangs over the edge of a 25 m building, as shown below: 25 BUILDING Ay = M₂ = y3 = 25 Y₂ = Y₁ The work required to pull the rope to the top of the building cannot be computed using the above formula because the distance each part of the rope must be moved is different! Answer the following questions and put your final answer for each part in the box. I. (The Approximate Work) A. On the figure above, the rope has been divided into three segments of equal length, Ay. Calculate Ay. d₂ = Yo ROPE B. Find the mass, M₂, of the middle segment of the rope. W₂ = y=0 C. The y values of the bottom of each segment of rope are indicated above. Find the values yo, y₁, and y2 and label them on the figure (No justification is necessary). By approximating that the middle segment is a particle located at y2: D. Find the distance d2 the middle segment must be moved to reach the top of the building. E. Find the approximate the work, W₂ required to move the middle segment to the top of the building by using the given formula. For computational convenience, take g = 10 m/s².
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