Question
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 26 kg, the acceleration of the object is 2 m/s. If the same force acts upon another object whose mass is 4 kg, what is this object's acceleration?
Answers
GPT-4o mini
To find the acceleration of the second object, we can use Newton's second law of motion, which states that \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.
First, we need to determine the constant force \( F \) acting on the first object (with mass 26 kg and acceleration 2 m/s²):
\[
F = m \cdot a = 26 \, \text{kg} \cdot 2 \, \text{m/s}^2 = 52 \, \text{N}
\]
Now that we know the force is 52 N, we can use this force to find the acceleration of the second object, which has a mass of 4 kg:
Using the same formula \( F = ma \), rearranging gives:
\[
a = \frac{F}{m}
\]
Substituting in the values we have:
\[
a = \frac{52 \, \text{N}}{4 \, \text{kg}} = 13 \, \text{m/s}^2
\]
Therefore, the acceleration of the 4 kg object when the same constant force acts upon it is:
\[
\boxed{13 \, \text{m/s}^2}
\]
First, we need to determine the constant force \( F \) acting on the first object (with mass 26 kg and acceleration 2 m/s²):
\[
F = m \cdot a = 26 \, \text{kg} \cdot 2 \, \text{m/s}^2 = 52 \, \text{N}
\]
Now that we know the force is 52 N, we can use this force to find the acceleration of the second object, which has a mass of 4 kg:
Using the same formula \( F = ma \), rearranging gives:
\[
a = \frac{F}{m}
\]
Substituting in the values we have:
\[
a = \frac{52 \, \text{N}}{4 \, \text{kg}} = 13 \, \text{m/s}^2
\]
Therefore, the acceleration of the 4 kg object when the same constant force acts upon it is:
\[
\boxed{13 \, \text{m/s}^2}
\]