1) based on this graph of force vs. extension for a certain spring, what should be the hooke's law constant (or spring constant)?

show the full calculation using data from the figure, and report the answer in n/m.

2) suppose a 250 g mass was hung from the spring in the previous question. what would be the extension of the spring when it is in equilibrium and at rest?

write the equation needed to answer this question and the solve for the extension, recording the answer in either m or cm.

3) now the 250 g mass hanging from the spring in the previous question is pulled down an extra 10 cm and released. what would be the period and the counting frequency of the oscillations?

once again, begin with an equation and show the steps needed to find the answers.

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.