To determine which box will have the greatest acceleration, we can use Newton's second law of motion, which states that acceleration (a) is equal to the net force (F) acting on an object divided by its mass (m). The formula is:
\[ a = \frac{F}{m} \]
We will calculate the acceleration for each scenario:
a. 20 kg box lifted with 40 N of force:
\[ a = \frac{40 , \text{N}}{20 , \text{kg}} = 2 , \text{m/s}^2 \]
b. 20 kg box lifted with 60 N of force:
\[ a = \frac{60 , \text{N}}{20 , \text{kg}} = 3 , \text{m/s}^2 \]
c. 10 kg box lifted with 40 N of force:
\[ a = \frac{40 , \text{N}}{10 , \text{kg}} = 4 , \text{m/s}^2 \]
d. 10 kg box lifted with 60 N of force:
\[ a = \frac{60 , \text{N}}{10 , \text{kg}} = 6 , \text{m/s}^2 \]
Now we compare the accelerations:
- a: \(2 , \text{m/s}^2\)
- b: \(3 , \text{m/s}^2\)
- c: \(4 , \text{m/s}^2\)
- d: \(6 , \text{m/s}^2\)
The box that will have the greatest acceleration is d: a 10 kg box lifted with 60 N of force with an acceleration of \(6 , \text{m/s}^2\).