Work, displacement, and gravity problem

In summary, the task at hand is to find the amount of work done by the hand and gravity on the book as it is lifted from a table to a bookshelf. Using the equation force*displacement=work, the force of gravity can be calculated by multiplying the mass of the book (1.4 kg) by the acceleration due to gravity (-9.8 m/s^2), resulting in a force of -13.7 N. This is then multiplied by the displacement of 1.4 m to get a work of -19 J, which is the work done by gravity on the book. To find the work done by the hand, the change in potential energy is used, as energy must be conserved. Therefore
  • #1
xgoddess210
27
0

Homework Statement



A 1.4 kg book is lying on a 0.80 m-high table. You pick it up and place it on a bookshelf 2.2 m above the floor.

1) How much work does your hand do on the book?

2.) How much work does gravity do on the book? [solved]

Homework Equations



Force*displacement=work

f=ma

The Attempt at a Solution



Ok. I was able to find the displacement to be 1.4 m. Since acceleration due to gravity is 9.8 (and negative in this case) i multiplied it by the mass 1.4 kg to get the force. Then I took the answer (-13.7) and multiplied that by the displacement which gave me the correct answer of -19 J.

The problem is that I', not sure how to find the amount of work the hand does on the book. The displacement is the same, but I don't know how to find the force. Any help would be appreciated.
 
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  • #2
Draw a free body diagram for the book to see the forces acting on it.

Another way to look at it is that in your system energy has to be conserved (work is a measure of energy)
 
  • #3
Your hand is providing all the work agianst gravity required to lift the book to it's new position. So the work your hand does is directly related to the change in potential energy. Can you see how?
 
  • #4
I think I'm starting to get it now. Thank you.
 

1. What is work and how is it calculated?

Work is defined as the force applied to an object multiplied by the distance the object moves in the direction of the force. It is calculated using the formula W = F * d, where W is work, F is force, and d is distance.

2. How do you find displacement in a given problem?

Displacement is a measure of an object's change in position. It can be calculated by subtracting the initial position from the final position. Alternatively, if the object's motion is in a straight line, it can be found by using the formula d = vf - vi, where d is displacement, vf is final velocity, and vi is initial velocity.

3. What is the relationship between work and displacement?

The relationship between work and displacement is that work is directly proportional to displacement. This means that when displacement increases, so does the amount of work done. Similarly, when displacement decreases, less work is done.

4. How does gravity affect work and displacement?

Gravity is a force that pulls objects towards the center of the Earth. As objects move against the force of gravity, work is done. The displacement of the object is also affected by gravity, as it determines the distance the object moves in the direction of the force.

5. Can you give an example of a work, displacement, and gravity problem?

One example of a work, displacement, and gravity problem could be calculating the work done by lifting a book off the ground and placing it on a shelf. The force applied is the weight of the book, the displacement is the height the book is lifted, and gravity is the force pulling the book towards the ground.

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