In the figure, two balls are located in deep space. The black ball has mass 56kg and the red ball has mass 17kg. The distance between the two balls is r=24cm.
(a) Find the magnitude of the acceleration of the red ball.
m/s2
(b) If r is 5 times larger, with what factor will the acceleration of the red ball change?
(c) If the mass of the black ball is 45 times larger, with what factor will the acceleration of the red ball change?
(d) If the mass of the red ball is 50 times larger, with what factor will the acceleration of the red ball change?
If you had shown some work, I would be willing to help. You are apparently using the service to harvest answers. Good luck.
i'm not sure how to begin the problem at all. Or else I would have shown some work. thanks though
(a) Get the force acting on each ball from Newton's universal law of gravity. That's whereto begin.
Force = G*M1*M2/r^2 (same for both balls)
G = universal constant
M1 = black ball mass
M2 = red ball mass
The acceleration of the red ball will be that force divided by the mass of the red ball.
(b) What happens when you multiply r by 5?
(c) 45
(d) a = Force/M2 is unchanged
thank you for your help! I really appreciate it.
To find the magnitude of the acceleration of the red ball, we can use Newton's law of universal gravitation. According to this law, the gravitational force between two objects is given by the equation:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force between the two objects,
G is the gravitational constant (approximately equal to 6.674 * 10^-11 N(m/kg)^2),
m1 is the mass of the first object,
m2 is the mass of the second object, and
r is the distance between the centers of the two objects.
(a) To find the magnitude of the acceleration of the red ball, we can use Newton's second law, which states that the force acting on an object is equal to its mass multiplied by its acceleration:
F = m * a
Where:
F is the gravitational force acting on the red ball,
m is the mass of the red ball, and
a is the acceleration of the red ball.
To find the acceleration of the red ball, we need to rearrange the equation for the gravitational force:
F = G * (m1 * m2) / r^2
m * a = G * (m1 * m2) / r^2
Since we are only interested in the magnitude of the acceleration, we can solve for it by rearranging the equation:
a = (G * m1 * m2) / (m * r^2)
Substituting the given values:
m1 = 56 kg (mass of the black ball)
m2 = 17 kg (mass of the red ball)
r = 24 cm = 0.24 m (distance between the two balls)
G ≈ 6.674 * 10^-11 N(m/kg)^2 (gravitational constant)
a = (6.674 * 10^-11 N(m/kg)^2 * 56 kg * 17 kg) / (17 kg * (0.24 m)^2)
Now, let's calculate the value of the acceleration:
a ≈ 0.082 m/s^2
Therefore, the magnitude of the acceleration of the red ball is approximately 0.082 m/s^2.
(b) If the distance between the two balls is 5 times larger than the initial distance, we need to calculate the new value of the acceleration using the same formula:
r' = 5 * r = 5 * 0.24 m = 1.2 m
a' = (G * m1 * m2) / (m * r'^2)
Substituting the known values:
a' = (6.674 * 10^-11 N(m/kg)^2 * 56 kg * 17 kg) / (17 kg * (1.2 m)^2)
Calculating the value of the new acceleration:
a' ≈ 0.0035 m/s^2
Therefore, the acceleration of the red ball changes by a factor of approximately 0.0035 m/s^2.
(c) If the mass of the black ball is 45 times larger than the initial mass, we need to calculate the new value of the acceleration using the same formula:
m1' = 45 * m1 = 45 * 56 kg
a' = (G * m1' * m2) / (m * r^2)
Substituting the known values:
a' = (6.674 * 10^-11 N(m/kg)^2 * (45 * 56 kg) * 17 kg) / (17 kg * (0.24 m)^2)
Calculating the value of the new acceleration:
a' ≈ 6.536 m/s^2
Therefore, the acceleration of the red ball changes by a factor of approximately 6.536 m/s^2.
(d) If the mass of the red ball is 50 times larger than the initial mass, we need to calculate the new value of the acceleration using the same formula:
m2' = 50 * m2 = 50 * 17 kg
a' = (G * m1 * m2') / (m * r^2)
Substituting the known values:
a' = (6.674 * 10^-11 N(m/kg)^2 * 56 kg * (50 * 17 kg)) / ((50 * 17 kg) * (0.24 m)^2)
Calculating the value of the new acceleration:
a' ≈ 0.328 m/s^2
Therefore, the acceleration of the red ball changes by a factor of approximately 0.328 m/s^2.