Final answer:
To find the magnitude of the acceleration of the particle, we can use Newton's Law of Universal Gravitation. The equation is F = G * (m1 * m2) / r^2. By calculating the forces between the particle and the two masses, and then summing them up, we can find the total force on the particle. Using F = ma, we can then calculate the magnitude of the acceleration.
Step-by-step explanation:
To find the magnitude of the acceleration of the particle, we can use Newton's Law of Universal Gravitation. The equation is:
F = G * (m1 * m2) / r^2
Where F is the gravitational force, G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the two point masses, and r is the distance between them.
In this case, the particle of mass m is released between the two masses, so its distance from the 8.75 kg mass is 17.0 cm. We can calculate the force between the particle and the 8.75 kg mass using the equation above, and then use Newton's second law (F = ma) to find the acceleration.
Let's calculate:
Distance from 8.75 kg mass to particle (r1) = 17.0 cm = 0.17 m
Distance from 14.0 kg mass to particle (r2) = distance between the two masses (50.0 cm = 0.5 m) - distance from 8.75 kg mass to particle (0.17 m) = 0.5 m - 0.17 m = 0.33 m
Force between particle and 8.75 kg mass (F1) = G * (m1 * m) / r1^2
Force between particle and 14.0 kg mass (F2) = G * (m2 * m) / r2^2
The total force on the particle is the sum of the forces from the two masses:
F_total = F1 + F2
Now we can use F_total = ma to find the acceleration:
a = F_total / m
Using the given values:
G = 6.67 x 10^-11 Nm^2/kg^2
m1 = 8.75 kg
m2 = 14.0 kg
r1 = 0.17 m
r2 = 0.33 m
m = given mass of the particle
Plug in the values and calculate the acceleration.