Answer:

Explanation:
a = Orbital radius = 
T = Orbital period = 23.21 hours
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
From Kepler's third law we get

From the given data the mass of Saturn is 
Answer:
It requires more tension to pull up the track
Explanation:
Net force must be zero to maintain constant velocity.
Weight force will always be pointed down the slope. Call it W
Friction force (Call it Ff) will be down slope when movement is up slope.
Friction force will be up slope when movement is down slope.
W and Ff are always positive numbers
Call the pulling force T
If Up slope is considered the positive direction
Moving up slope
Tu - Ff - W = 0
Tu = Ff + W
Moving down slope
Td + W - Ff = 0
Td = Ff - W
Ff + W > Ff - W therefore Tu > Td
Answer:
This depends on what angle they are approaching each other before they collided.The two simple cases are if they are running in the same direction or opposite direction from each other. For either case, use the conservation of momentum equation to solve: M_total*V_result = M1*V1 + M2*V2
Explanation:
Here are two possible solutions.
Head-on collision: M1=78, V1=8.5, M2=72, V2=-7.5 (that's negative because he's running the other way), M_total = 78+72 = 150, so V_result = (78*8.5 - 72*7.5)/150 = 0.82 m/s. Sanity check, they weigh about the same and so most of their velocity should cancel out.
Running the same way: change the sign of V2 to positive so V_result = (78*8.5 + 72*7.5)/150 = 8.02 m/s. Sanity check, they weigh about the same and the resultant speed is between the two starting velocities.
<em>hope it helps:)</em>
There are two interchangeable concepts that can be applied to this theory. The first one is the moment of Inertia and the second the perioricity. When the runners put their leg forward they reduce their moment of inertia allowing their center of mass to maintain the speed they carry and not waste energy. In this way when they swing, the leg begins to act as a kind of pendulum, and remember that the pendulum is directly proportional to the length, that is,

In this way, by bringing their legs closer they reduce the distance and make the period shorter.