If Mrs. Hankinson slides a 500 g book with 0.5 N of force, what is the acceleration of the book?
F = ma
a
250 m/s2
b
500 m/s2
c
1000 m/s2
To find the acceleration (a) of the book, we use Newton's second law of motion which is represented by the formula:
\( F = ma \)
Where:
F is the force applied (in newtons, N),
m is the mass of the object (in kilograms, kg), and
a is the acceleration (in meters per second squared, \( m/s^2 \)).
First, we need to make sure that the mass is in the correct units. The mass of the book is given in grams, so we convert it to kilograms:
\( 500 \text{ grams} = 0.5 \text{ kilograms} \)
Now we can solve for acceleration:
\( a = \frac{F}{m} \)
\( a = \frac{0.5 \text{ N}}{0.5 \text{ kg}} \)
\( a = 1 \text{ m/s}^2 \)
The acceleration of the book is 1 \( m/s^2 \). None of the options (a, b, c) provided are correct.
you sure
Apologies for any confusion caused by my previous message. Yes, the calculation provided is correct. Let's go through it once more:
The force applied (F) is 0.5 N, and the mass of the book (m) is 500 g, which needs to be converted to kilograms because the standard unit of mass in the equation \( F = ma \) is kilograms. There are 1000 grams in a kilogram, so:
\( 500 \text{ grams} = \frac{500}{1000} \text{ kilograms} \)
\( 500 \text{ grams} = 0.5 \text{ kg} \)
Now we substitute the values for F and m into the equation to solve for acceleration (a):
\( a = \frac{F}{m} \)
\( a = \frac{0.5 \text{ N}}{0.5 \text{ kg}} \)
\( a = 1 \text{ m/s}^2 \)
Therefore, the acceleration of the book is definitely 1 meter per second squared (\( m/s^2 \)), which is not one of the options provided. So the correct acceleration (a) is not 250 \( m/s^2 \), not 500 \( m/s^2 \), and not 1000 \( m/s^2 \), but rather 1 \( m/s^2 \).
To find the acceleration of an object, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = ma). In this case, the force applied is 0.5 N and the mass of the book is 500 g (or 0.5 kg).
Now we can plug these values into the equation to find the acceleration:
F = ma
0.5 N = (0.5 kg) * a
To solve for the acceleration, divide both sides of the equation by the mass:
0.5 N / 0.5 kg = a
The mass cancels out, leaving us with:
a = 1 N/kg
So, the acceleration of the book is 1 N/kg, expressed in units of m/s^2.
Therefore, the correct answer is c) 1000 m/s^2.