A solid uniform sphere has a mass of 2.0 104 kg and a radius of 1.5 m. What is the magnitude of the gravitational force due to the sphere on a particle of mass m = 0.2 kg located at a distance of 1.6 m from the center of the sphere? What if it is 1.1 m from the center of the sphere?
Use the universal law of gravity
F = G M m /R^2,
where G is the universal gravitational constant and R is the separation distance between the center of the sphere and the particle. M amd m are the masses of the sphere and the particle, respectively. Consider the "particle" to be a point source.
In the first case, R = 1.6 m. In the second case, the particle is inside the sphere, and only the mass of the larger sphere that is inside r = 1.1 m contributes a net gravitational attraction. For that case, use M = 2.0*10^4 * (1.1/1.5)^3, since that is the mass inside r = 1.1 m.
Ok thanks a lot!!!
To find the magnitude of the gravitational force due to the sphere on a particle, we can use the universal law of gravity equation:
F = G * M * m / R^2
Where:
- F is the gravitational force
- G is the universal gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
- M is the mass of the sphere
- m is the mass of the particle
- R is the separation distance between the center of the sphere and the particle
Let's calculate the gravitational force for both cases:
First case:
M = 2.0 * 10^4 kg (given mass of the sphere)
m = 0.2 kg (given mass of the particle)
R = 1.6 m (given separation distance)
Plugging the values into the equation, we have:
F = (6.67430 × 10^-11 N m^2/kg^2) * (2.0 * 10^4 kg) * (0.2 kg) / (1.6 m)^2
Calculating this equation gives the magnitude of the gravitational force.
Second case:
In this case, the particle is inside the sphere at a distance of 1.1 m from the center. Only the mass of the larger sphere inside the radius of 1.1 m contributes to the net gravitational attraction.
M = 2.0 * 10^4 kg * (1.1/1.5)^3
We use (1.1/1.5)^3 to account for the ratio of the mass inside the radius of 1.1 m to the total mass of the sphere. This gives us the effective mass inside the radius.
Then, we can calculate the gravitational force using the same equation as before, but with this updated value for M.
I hope this explanation helps you understand the process of calculating the gravitational force. If you have any further questions, feel free to ask!