How do I solve these physics problems involving gravity and circular motion?

[godemiche]

Just a LIL Physics Help :)

Some odds of my homework I couldn't figure out,,, any help would be appreciated and REPPED

1.
Find the centripetal accelerations of a point on the Equator, due to the rotation of Earth about its axis.
m/s2

2.
Two objects attract each other with a gravitational force of magnitude 0.99 10-8 N when separated by 19.6 cm. If the total mass of the two objects is 5.08 kg, what is the mass of each?
kg (heavier mass)
kg (lighter mass)

3.
A satellite moves in a circular orbit around the Earth at a speed of 5458 m/s.
(a) Determine the satellite's altitude above the surface of the Earth.
m
(b) Determine the period of the satellite's orbit.
h

if needed
mass of Earth = 5.98 E 24
Radius of Earth = 6.38 E 6
G = 6.67 E -11

 

[Nenad]

for 1. use the equation a_c = \frac{v^2}{r} to find a, you need to find out at what speed you are rotating at. Thisnk about it, you know how long a day is, you know the Earth's radius. Solve the problem.

for 2. use Newtons law of gravitational attraction: F_g = \frac{Gm_{1} m_{2}}{d^s} you know the distance between the two, you know the G constant, you have the force. To solve for the mass inequality, just set up an equation for mass using 5.08-x and x as your two masses. Now solve for x.

3. Ill let you ponder on that one by yourself. I alwready solved the first two for you, which I shouldn't have.

Regards,

Nenad

 

[thepatientmental]

1. To solve this problem, you can use the formula for centripetal acceleration: a = v^2/r, where v is the velocity and r is the radius of the circular motion. In this case, the velocity is equal to the speed of rotation of Earth, which is approximately 463 m/s at the Equator. The radius of the circular motion is equal to the radius of Earth, which is 6.38 E 6 m. Plugging in these values into the formula, we get a = (463 m/s)^2/6.38 E 6 m = 0.034 m/s^2. This is the centripetal acceleration of a point on the Equator due to the rotation of Earth.

2. To solve this problem, we can use the formula for gravitational force: F = G(m1m2)/r^2, where G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them. We know that the force is 0.99 10-8 N and the distance is 19.6 cm = 0.196 m. Plugging in these values and the given mass of 5.08 kg for the total mass, we get 0.99 10-8 N = (6.67 E -11)(5.08 kg)(m2)/ (0.196 m)^2. Solving for m2, we get m2 = 1.06 kg. Since the total mass is 5.08 kg, the mass of the other object must be 5.08 kg - 1.06 kg = 4.02 kg.

3. To solve this problem, we can use the formula for centripetal force: F = m(w^2)r, where m is the mass of the satellite, w is the angular velocity, and r is the distance from the center of the Earth. We know that the force of gravity is balanced by the centripetal force, so we can set them equal to each other: G(m1m2)/r^2 = m(w^2)r. We also know that the angular velocity is equal to the speed of the satellite divided by the radius of its orbit, so w = v/r. Plugging in the given values, we get G(m1m2)/r^2 = m(v^2)/r^