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1. How much does the ball weight in water

write the eqn for beaker and ball as a system and note that the only force acting on them is the force of tension in string(connected to ball)and Normal(the weight measured) Find tension using eqm of ball
2. Question on Momentum, Force and Impulse

I think you should think that since an impulsive force has acted on car,we cannot use Conservation of Momentum.The final momentum is $0$. Change in momentum is same in both the cases,but 'rate of change of momentum' is different and thus,the forces are different.
3. Angles and graphs, basic question

yes,why not. :) Angle between lines joining (x_1,y_1) \&\(x_2,y_2)=tan^{-1}\left( \frac{y_2-y_1}{x_2-x_1}\right)
4. Motion problem - Shock drop ride

hello,I suppose you'ld not need most of the data given. We can assume g=10ms^{-2} now we know distance covered,the acceleration,the initial velocity. Just put in formulas
5. Momentum help.

hello, such questions can be solved using Conservation Of Momentum,and Work Energy theorem(that you used) 1st derive a relation between velocities of masses(call v_1\ and\ v_2) then use the equation you are using thanks
6. Work Conceptual Questions

hello, just check http://en.wikipedia.org/wiki/Mechanical_work" [Broken] I suppose,it helps. Dot product of two vectors is scalar :smile:
7. Using the angle of a pendulum to measure the acceleration of a plane.

hello, I'ld advise you to check for http://en.wikipedia.org/wiki/Fictitious_force" [Broken] as you are in Accelerated frame of reference. Here the forces acting on the bob are tension,weight and pseudo force(if you write equation in aeroplane frame of reference).Break Tension in horizontal...