Mechanics | Relativity Answers

A rock weighs 130 N in air and has a volume of 0.00331 m3.
What is its apparent weight when sub- merged in water? The acceleration of gravity is 9.8 m/s2 .

A ferry boat is 6.1 m wide and 7.1 m long. When a truck pulls onto it, the boat sinks 7.59 cm in the water.
What is the weight of the truck? The acceleration of gravity is 9.81 m/s2 .
Answer in units of N

A fox fleeing from a hunter encounters a 0.730 m tall fence and attempts to jump it. The fox jumps with an initial velocity of 7.10 m/s at an angle of 45.0°, beginning the jump 2.11 m from the fence. By how much does the fox clear the fence? Treat the fox as a particle.

(a) Suppose A= (5,0) and B=(0,12). write C1 =A+B in polar corrdinates (r,θ) . i got this covered. it should be (13,67.4 degrees north of east).

the problem i have here is
(b) C2=(6,45 degresss north of east). Write C2 in the forms of ( C, θc) and (Cx,Cy).

I thought (C,θc) is already given while (Cx,Cy) doesnt make sense to me. I learned that Cx=Ax+Bx which is 5 but it is given to be 6?

A ball rolls off a frictionless sphere with neglible inital velocity, at what point does the ball fall off?

During a baseball game a batter hits a long flyball. If the ball remains in the air for 6.0 sec, how high does it rise?

what volume is displaced by a piece of steel weighing 200 kg floating in a lake? ( The density of steel is 7860kgm^-3 )

a piece of metal weighs 75N in air and 60 N in water what is the buoyant force acting on the metal?

I would be grateful if you might help me with a difficult problem in mechanics that I have tried to solve for a long time without success:

How much power P [W] is needed to force a satellite (modeled as a point particle) to move in a perfect circular orbit with radius r [m]? The mass of the satellite is m [kg] and its tangential speed v [m/s] is constant.

Important conditions:
- It is assumed that NO GRAVITY affects the satellite!
- The mass loss due to fuel consumption is neglected.
- The power is assumed to act under ideal conditions, i.e. there is no energy loss due to friction or the choice of engine.
- Relativistic effects are neglected.

I have received many answers saying that P = 0 as a consequence of the definition of mechanical work. But this cannot be true since no gravity affects the satellite. Energy is needed to create a force that changes a linear path in space and a circular orbit is one such motion. In absence of gravity no particle with mass will loop in a circle without any energy.

A box of books is initially at rest a distance D = 0.600 m from the end of a wooden board. The coefficient of static friction between the box and the board is μs = 0.324, and the coefficient of kinetic friction is μk = 0.248. The angle of the board is increased slowly, until the box just begins to slide; then the board is held at this angle. Find the speed of the box as it reaches the end of the board.