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?
If it weighs 36 pounds on Callisto it exerts a force of 36 pounds on Callisto
toward the box from the center of the moon.
Pounds is FORCE, not mass, and if you weighed it in pounds on Callisto with a scale, that is the gravitational force on it there.
To determine the force exerted by the box on Callisto, we need to use Newton's second law of motion. According to this law, the force (F) is equal to the product of mass (m) and acceleration (a). However, in this case, the weight of the box can be used as a substitute for the mass, as weight is the force of gravity acting on an object.
1. Calculate the weight of the box on Callisto:
The weight of an object can be calculated using the formula: weight = mass × acceleration due to gravity.
Since we are given the weight of the box as 36 lb, we can directly proceed to the next step.
2. Determine the acceleration due to gravity on Callisto:
The value of acceleration due to gravity varies from planet to planet or moon to moon. On Callisto, the acceleration due to gravity is approximately 1.25 m/s^2 or 0.041 ft/s^2.
3. Calculate the force exerted by the box on Callisto:
Using the formula F = m × a and substituting the weight of the box, we have:
F = weight × acceleration due to gravity.
In this case, the weight is 36 lb and the acceleration due to gravity is approximately 0.041 ft/s^2 (or 1.25 m/s^2). Thus,
F = 36 lb × 0.041 ft/s^2.
After performing the multiplication, we find that the force exerted by the box on Callisto is approximately 1.476 lb-ft/s^2.
Now, let's discuss the direction of the force. Since the box is falling freely on Callisto, the force exerted by the box is in the downward direction (towards the moon's center). This is because the gravitational force always acts towards the center of the celestial body.