A box is on Callisto (2nd largest moon of Jupiter). The box weighs 36 lb and is in free fall. How much force is the box exerting on Callisto and in what direction?
To calculate the force the box is exerting on Callisto, we need to use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the mass of the box remains constant at 36 lb (lbs), but we need to calculate the acceleration due to gravity on Callisto.
1. First, we need to convert the weight of the box from pounds (lb) to mass in terms of kilograms (kg).
- The conversion factor to convert pounds to kilograms is 1 lb ≈ 0.4536 kg.
- So, the mass of the box in kilograms (m) is: 36 lb × 0.4536 kg/lb ≈ 16.3296 kg.
2. Next, we need to determine the acceleration due to gravity on Callisto.
- The acceleration due to gravity on Callisto is approximately 1.24 m/s².
- This means that for every kilogram of mass, an object will experience a force of 1.24 newtons (N).
3. Now, we can calculate the force exerted by the box on Callisto.
- Force (F) = mass (m) × acceleration (a)
- F = 16.3296 kg × 1.24 m/s² ≈ 20.25 N.
Therefore, the box is exerting a force of approximately 20.25 Newtons on Callisto in the downward direction (toward the center of Callisto), since the force of gravity always acts downward.