Exercise 1) A block of ice slides down a frictionless ramp at angle θ = 50°, while an ice worker pulls up the ramp (via a rope) with a force of magnitude Fr = 40 N. As the block slides through distance d = 0.65 m along the ramp, its kinetic energy increases by 78 J. How much greater would its kinetic energy have been if the rope had not been attached to the block?
Exercise 2) A constant force of magnitude 82.0 N is applied to a 2.95 kg shoe box at angle ? = 51.5°, causing the box to move up a frictionless ramp at constant speed. How much work is done on the box by a when the box has moved through vertical distance h = 0.155 m?
Exercise 3) A 1.8 kg block is initially at rest on a horizontal frictionless surface when a horizontal force in the positive direction of an x axis is applied to the block. The force is given by (x) = (2.2 - x2) N, where x is in meters and the initial position of the block is x = 0.
(a) What is the kinetic energy of the block as it passes through x = 1.9 m?
(b) What is the maximum kinetic energy of the block between x = 0 and x = 1.9 m?
Exercise 4) A single force acts on a 4.0 kg particle-like object in such a way that the position of the object as a function of time is given by x = 3.0t - 4.0t 2 + 1.0t 3, with x in meters and t in seconds. Find the work done on the object by the force from t = 0 to t = 7.0 s.
Exercise 5) A force of 6.0 N acts on a 14 kg body initially at rest.
(a) Compute the work done by the force in the first second.
(b) Compute the work done by the force in the second second.
(c) Compute the work done by the force in the third second.
(d) Compute the instantaneous power due to the force at the end of the third second.
Exercise 6) To push a 27.0 kg crate up a frictionless incline, angled at 25.0° to the horizontal, a worker exerts a force of 228 N, parallel to the incline. Assume that the crate slides 1.50 m.(a) What is the work done on the crate by the worker's applied force?
(b) What is the work done by the gravitational force on the crate?
(c) What is the work done by the normal force exerted by the incline on the crate?
(d) What is the total work done on the crate?
Exercise 7) In the ammonia (NH3) molecule of the figure, the three hydrogen (H) atoms form an equilateral triangle, with the center of the triangle at distance d = 9.40 ? 10-11 m from each hydrogen atom. The nitrogen (N) atom is at the apex of a pyramid, with the three hydrogen atoms forming the base. The nitrogen-to-hydrogen atomic mass ratio is 13.9, and the nitrogen-to-hydrogen distance is L = 10.14 ? 10-11 m.