How Do You Calculate Gravitational Forces and Friction in Physics Problems?

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The discussion revolves around calculating gravitational forces and friction in various physics problems. It includes scenarios such as determining the gravitational force between two parts of a space probe, calculating gravitational acceleration for satellites in orbit, and analyzing frictional forces on a box in an elevator under different conditions. Additionally, it covers the coefficient of static and kinetic friction for a crate on an inclined ramp, as well as the stopping time for a car with locked wheels. Participants emphasize the importance of showing prior work to facilitate effective assistance.
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1:On earth, two parts of a space probe weigh 12900 N and 4590 N. These parts are separated by a center-to-center distance of 5.15 m and may be treated as uniform spherical objects. Find the magnitude of the gravitational force that each part exerts on the other out in space, far from any other objects.

2:Synchronous communications satellites are placed in a circular orbit that is 4.37 x 108 m above the surface of the earth. What is the magnitude of the acceleration due to gravity at this distance?

3:A 4.42-kg box is sliding across the horizontal floor of an elevator. The coefficient of kinetic friction between the box and the floor is 0.392. Determine the kinetic frictional force that acts on the box when the elevator is (a) stationary, (b) accelerating upward with an acceleration whose magnitude is 1.79 m/s2, and (c) accelerating downward with an acceleration whose magnitude is 1.79 m/s2.

4:A crate is resting on a ramp that is inclined at an angle above the horizontal. As is increased, the crate remains in place until reaches a value of 31.1°. Then the crate begins to slide down the slope. (a) Determine the coefficient of static friction between the crate and the ramp surface. (b) The coefficient of kinetic friction between the crate and the ramp is 0.380. Find the acceleration of the moving crate.

5:Traveling at a speed of 10.3 m/s, the driver of an automobile suddenly locks the wheels by slamming on the brakes. The coefficient of kinetic friction between the tires and the road is 0.670. How much time does it take for the car to come to a halt? Ignore the effects of air resistance.
 
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Please show what you've tried.
 
Im having trouble with these questions .. wud anyone please help me out ?

Thank you
 
It's difficult to help until you show what you've done so far. That's the only way to see what you know and don't know and to pinpoint any errors you may be making.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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