Physics problems, need help ASAP

[ahmed]

Q1   
In Fig. 8-33(pic. attached below), a frictionless roller-coaster car of mass tops the first hill with speed at height . How much work does the gravitational force do on the car from that point to (a) point A, (b) point B, and (c) point C? If the gravitational potential energy of the car–Earth system is taken to be zero at C, what is its value when the car is at (d) B and (e) A? (f) If mass m were doubled, would the change in the gravitational potential energy of the system between points A and B increase, decrease, or remain the same?

Q2
   
What are (a) the x coordinate and (b) the y coordinate of the center of mass for the uniform plate shown in Fig. 9-38(pic. attached) if L=5 cm?

Q3
    
Figure 9-56(pic. attached) shows an approximate plot of force magnitude F versus time t during the collision of a 58 g Superball with a wall. The initial velocity of the ball is 34 m/s perpendicular to the wall; the ball rebounds directly back with approximately the same speed, also perpendicular to the wall. What is Fmax, the maximum magnitude of the force on the ball from the wall during the collision?

[Mao]

Q1:

In this case, gravity is the only force doing acting on the roller coaster. Then, the work done by gravitational force is the change in gravitational potential energy.

to point A: no work done, GPE = 0
to point B: mgh/2, GPE = -mgh/2
to point C: mgh, GPE = -mgh

If the mass was doubled, gravity would do twice as much work, hence the change in GPE between A and B would increase.

Q2
remembering that and ,

simplifying each block as particles:
In first quadrant, a mass of at (2,2.5)
In second quadrant, a mass of at (-1,1.5)
In third quadrant, a mass of at (-1,-2)
In fourth quadrant, a mass of at (1,-3)

Hence,



Q3
the net impulse is the net change in momentum, that is



.