You need to pick up a book off the floor and place it on a table top that is 0.78 m above ground. You expend 1.56 J of energy to lift the book. The book has an acceleration of 1.54 m/s squared. What is the book's mass?
m g h = gain in potential energy
so
m (9.81)( .78) = 1.56
or
m = 1.56/(9.81*.78)
If it asked for the force, you could now do F = m a
The energy used to raise the book is m*g*h = 1.56J. I don't understand the rest. What weight?
It does not mention weight, only asked for m
There is no need to use a = 1.54 as the problem is stated.
I bet there is a part B though that asks for the average force
Then
F - m g = m (1.54)
oh ok yeah your right
To find the book's mass, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m * a). In this case, the force is the gravitational force acting on the book as it accelerates upward.
First, let's find the force acting on the book. We know that the force is equal to the weight of the book, which can be calculated using the formula weight = mass * gravitational acceleration.
The gravitational acceleration on Earth is approximately 9.8 m/s². So, the weight of the book can be found by multiplying the gravitational acceleration by its mass:
Force = weight = m * g
Now, let's calculate the force acting on the book by dividing the energy expended to lift the book by the distance lifted:
Force = energy / distance
Force = 1.56 J / 0.78 m = 2 J/m
Since Force = m * a, we can substitute the values:
m * a = 2 J/m
Rearranging the equation, we have:
m = 2 J/m / a
Now, substituting the given values:
m = 2 J/m / 1.54 m/s²
m ≈ 1.30 kg
Therefore, the book's mass is approximately 1.30 kg.