Three masses, m1 (a mouse), m2 (a bear) and m3 (an elephant), are in circular orbits of radii r1, r2 and r3 around the sun. The masses obey the relation, m1 < m2 < m3. While r1 and r2 are equal to Earth's orbital radius, r3 is equal to Jupiter's orbital radius.
1) The orbital period of m3 is ____________________ the orbital period of m2.
A) greater than
2) The orbital period of m2 is ____________________ the orbital period of m1.
A) equal to
3) The magnitude of the acceleration of m2 is _____________ the magnitude of the acceleration of m1.
A) equal to
4) The magnitude of the gravitational force acting on m2 is ____________________ the magnitude of the gravitational force acting on m1.
A) greater than
How do you figure out 4? And, I got the other 3 correct but I'm not sure if I just guessed lucky.
What's the best way to do this?
all correct.
One way to think on four is to stop considering "g" as acceleration as in three. In the equation
gravitational force= mass*g
consider g to be gravitational field strength, in newtons/kg. In Earths case, g at the surface is 9.8N/kg
Using this thinking, then if the mass m2>m1, gravitational force= m2*g , so the force on m2 is greater than on m1 because its mass is greater.
In 4, both masses are the same distance from the (same) sun. Force is proportional to mass, so m2 has the greater force from the sun.
To answer question 4, you need to consider the relationship between the magnitude of the gravitational force and the masses and radii involved. Here's how you can figure it out:
The gravitational force between two masses is given by Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
Where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between the center of masses of the two objects.
In this case, we want to compare the magnitude of the gravitational force acting on m2 (bear) and m1 (mouse).
Let's assume m1 = M1 and r1 = R (Earth's orbital values), and m2 = M2 and r2 = R (Earth's orbital values).
G, the gravitational constant, is a universal constant and remains constant.
To compare the gravitational forces, we can set up the following ratio:
F2 / F1 = (G * (M2 * Msun) / r2^2) / (G * (M1 * Msun) / r1^2)
Since G, the gravitational constant and Msun, the mass of the Sun, are common in both fractions, we can cancel them out. Also, since r1 = r2, we can simplify further:
F2 / F1 = (M2 * r1^2) / (M1 * r2^2)
From the given information, we know that M2 > M1, which means that the numerator (M2 * r1^2) will be larger than the denominator (M1 * r2^2).
Therefore, the magnitude of the gravitational force acting on m2 (bear) is greater than the magnitude of the gravitational force acting on m1 (mouse).
Hence, the answer to question 4 is A) greater than.