Newton's law of universal gravitation is represented by F= G* Mm/ T where F is the gravitational force, M and m are masses, and r is a length. Force has the Sl units kg • m/s?. What are the Sl units of the proportionality constant G? Show the work.

A 9.00-kg particle moves from the origin to position ©, having coordinates x = 4.50 m and y = 4.50 m as shown in the figure. One force on the particle is the gravitational force acting in the negative y direction. Using the equation (W = FAr cos e = F . Ař), calculate the work done by the gravitational force in going from O to © along the following paths. у (m) C) (x, y) х (m) (a) the purple path (o0© (b) the red path (OB© (c) the blue path (O© (d) Your results should all be identical. Why?

A mountain climber is about to haul up a 90-m length of hanging rope. How much work will it take if the rope weighs 0.65 N/m? Set up the integral that gives the work done. (Type an exact answer, using radicals as needed.)

Force = 4x ^ 4 - 3x. Find the work in mks units done by the force for a distance of x = 1 to x = 7:

When a spring is compressed by 2.0 cm, its spring potential energy is 16.9 J. What will its spring potential energy be if it is stretched by 4.0 cm, in Joule? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.