A 1.1 kg book is lying on a 0.77 m -high table. You pick it up and place it on a bookshelf 2.3 m above the floor.
1. How much work does gravity do on the book?
2. How much work does your hand do on the book?
How do you find work?
work done is equal to the change of graviational potential energy here: mgh
In general, work is force*distance*cosineAnglebetween force and distance.
2.6
To find the work done, you need to use the equation:
Work = Force × Distance × cos(θ)
Where:
- Work is the energy transferred or expended by a force.
- Force is the magnitude of the force applied.
- Distance is the displacement of the object in the direction of the applied force.
- θ is the angle between the force and the direction of displacement.
1. How much work does gravity do on the book?
The force applied by gravity can be calculated using the equation:
Force of gravity = mass × acceleration due to gravity
Given that the mass of the book is 1.1 kg and the acceleration due to gravity is approximately 9.8 m/s², you can calculate the force of gravity:
Force of gravity = 1.1 kg × 9.8 m/s²
Once you have the force of gravity, you need to find the distance the book moves. In this case, we are lifting the book from the table to the bookshelf, which is a height difference of 2.3 m - 0.77 m = 1.53 m.
Now, plug the values into the equation for work:
Work = Force × Distance × cos(θ)
Since the force of gravity acts vertically downward along the displacement, the angle between the force and displacement (θ) is 0°. Therefore, cos(0°) = 1.
Work = (Force of gravity) × (Distance) × cos(0°)
Calculate the work done by gravity.
2. How much work does your hand do on the book?
When you lift the book, your hand applies a force equal in magnitude but opposite in direction to the force of gravity. The distance your hand applies the force is the same as the distance mentioned earlier, 1.53 m.
Plug these values into the same equation for work:
Work = Force × Distance × cos(θ)
Since the force applied by your hand is opposite to the displacement, the angle between the force and displacement (θ) is 180°. Therefore, cos(180°) = -1.
Work = (Force) × (Distance) × cos(180°)
Calculate the work done by your hand.
Remember, work is measured in joules (J), which is the unit of energy. Positive work means energy is transferred to the object, while negative work means energy is taken away from the object.