A 1.5 kg book is lying on a 0.70 m -high table. You pick it up and place it on a bookshelf 2.0 m above the floor.
During this process, how much work does gravity do on the book?
-> 1.5 * -9.8 * 1.3 = -19.1 J
During this process, how much work does your hand do on the book?
-19.1
To calculate the work done by your hand on the book, we need to consider the change in gravitational potential energy of the book when it is lifted from the table to the bookshelf.
The formula to calculate the work done is:
Work = Force x Distance x Cos(theta)
In this case, the force exerted by your hand to lift the book is equal to the weight of the book, which can be calculated by multiplying the mass of the book (1.5 kg) by the acceleration due to gravity (-9.8 m/s^2).
So the force, F = m x g = 1.5 kg x (-9.8 m/s^2) = -14.7 N
The distance through which the force is applied is the vertical distance from the table to the bookshelf, which is 2.0 m.
Substituting the values into the formula:
Work = -14.7 N x 2.0 m x Cos(180 degrees) = -29.4 J
Therefore, your hand does -29.4 Joules of work on the book. The negative sign indicates that the work is done against gravity, as you are lifting the book upwards.