A ball is thrown vertically upwards with a speed of 15 ms

Question

Question 1: What is the velocity required to escape the earth's gravitational attraction. (Note: M_Earth = 5.97 x 10²⁴ kg and R_Erath = 6.37 x 10₆ m)

Question 2: A sphere a filled cylinder and a hollow cylinder of inner radius R/2, all with a mass M and radius R, if all three starts from rest find the ratio of the speed of the sphere v_sphere to the speed of the hollow cylinder V_cylinder.

Question 3: A mass m sitting on a frictionless table has an initial speed v_i. The mass is attached to a piece of string that is being acted on by a force F^→ at the center. Find the speed of the mass when the radius of the string decreases to r.

Question 4: A ball is thrown vertically upwards with a speed of 15 m/s from the ground. At the same instant of time a second ball is thrown vertically upwards with a speed v₀ from a height of 30m above the first ball. If both land at the same time, what is the speed v₀ of the second ball?

Question 5: A mass m is pushed down an incline, compressing a spring a distance d. When released find an expression for the speed the mass will reach when the spring is uncompressed. Assume the incline is frictionless.

Question 6: If a particular force has a potential energy U(x) = 9x² - 0.5 x⁴. Find the force at a position x = 3m.