Questions: A student lifts a 2.4-kg physics book to a height of 38 cm and then puts it down to its original position. Assume that the speed of the book remains constant during the entire process. The work done by the student while lifting the book up, w1= Units Select an answer. The work done by the gravity force while lifting the book up, w2= Units Select an answer. The work done by the student while putting the book down, w3= Units Select an answer. The work done by the gravity force while putting the book down, w4= Units Select an answer. If the book is lifted up in 1.2 seconds, how much power was developed by the student? P= Units Select an answer.

A student lifts a 2.4-kg physics book to a height of 38 cm and then puts it down to its original position. Assume that the speed of the book remains constant during the entire process. The work done by the student while lifting the book up, w1= Units Select an answer. The work done by the gravity force while lifting the book up, w2= Units Select an answer. The work done by the student while putting the book down, w3= Units Select an answer. The work done by the gravity force while putting the book down, w4= Units Select an answer. If the book is lifted up in 1.2 seconds, how much power was developed by the student? P= Units Select an answer.
Transcript text: A student lifts a $2.4-\mathrm{kg}$ physics book to a height of 38 cm and then puts it down to its original position. Assume that the speed of the book remains constant during the entire process. The work done by the student while lifting the book up, $\mathrm{w}_{1}=$ $\square$ Units Select an answer $\vee$. The work done by the gravity force while lifting the book up, $w_{2}=$ $\square$ Units Select an answer $\vee$. The work done by the student while putting the book down, $\mathrm{w}_{3}=$ $\square$ Units Select an answer $\vee$. The work done by the gravity force while putting the book down, $\mathrm{w}_{4}=$ $\square$ Units Select an answer $\vee$. If the book is lifted up in 1.2 seconds, how much power was developed by the student? $P=$ $\square$ Units Select an answer $\vee$.
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Solution

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Solution Steps

Step 1: Calculate the Work Done by the Student While Lifting the Book

The work done by the student while lifting the book is equal to the gravitational potential energy gained by the book. This can be calculated using the formula: \[ w_1 = m \cdot g \cdot h \] where:

  • \( m = 2.4 \, \text{kg} \) is the mass of the book,
  • \( g = 9.81 \, \text{m/s}^2 \) is the acceleration due to gravity,
  • \( h = 0.38 \, \text{m} \) is the height the book is lifted.

Substituting the values, we get: \[ w_1 = 2.4 \cdot 9.81 \cdot 0.38 = 8.9431 \, \text{J} \]

Step 2: Calculate the Work Done by Gravity While Lifting the Book

The work done by the gravitational force while lifting the book is equal in magnitude but opposite in direction to the work done by the student. Therefore: \[ w_2 = -m \cdot g \cdot h = -8.9431 \, \text{J} \]

Step 3: Calculate the Work Done by the Student While Putting the Book Down

When the book is put down, the work done by the student is equal in magnitude but opposite in direction to the work done while lifting. Therefore: \[ w_3 = -m \cdot g \cdot h = -8.9431 \, \text{J} \]

Step 4: Calculate the Work Done by Gravity While Putting the Book Down

The work done by gravity while putting the book down is equal in magnitude and direction to the work done by the student while lifting the book. Therefore: \[ w_4 = m \cdot g \cdot h = 8.9431 \, \text{J} \]

Step 5: Calculate the Power Developed by the Student

Power is defined as the work done per unit time. The power developed by the student while lifting the book can be calculated using the formula: \[ P = \frac{w_1}{t} \] where \( t = 1.2 \, \text{s} \) is the time taken to lift the book.

Substituting the values, we get: \[ P = \frac{8.9431}{1.2} = 7.4526 \, \text{W} \]

Final Answer

  • The work done by the student while lifting the book: \(\boxed{8.9431 \, \text{J}}\)
  • The work done by gravity while lifting the book: \(\boxed{-8.9431 \, \text{J}}\)
  • The work done by the student while putting the book down: \(\boxed{-8.9431 \, \text{J}}\)
  • The work done by gravity while putting the book down: \(\boxed{8.9431 \, \text{J}}\)
  • The power developed by the student: \(\boxed{7.4526 \, \text{W}}\)
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