To move a large crate across a rough floor, you push on it with a force F at an angle of 21 degrees below the horizontal, Find the force necessary to start the crate moving, given that the mass of the crate is 32 kg and the coefficient of static friction between the crate and the floor is 0.53.

Which statement is true? a. kepler's laws apply only to the motion of earth. b. kepler's laws can be used to predict eclipses. c. kepler's laws are true for a central force that is directly proportional to distance. d. kepler's laws can be deduced from newton's laws of motion and gravity.

Charge is distributed along the entire x-axis with uniform density λ. how much work does the electric field of this charge distribution do on an electron that moves along the y-axis from y = a to y = b? (use the following as necessary: a, b, ε0, λ, and q for the charge on an electron.)

Aspring is used to stop a 50-kg package which is moving down a 20º incline. the spring has a constant k = 30 kn/m and is held by cables so that it is initially compressed 50 mm. knowing that the velocity of the package is 2 m/s when it is 8 m from the spring and neglecting friction, determine the maximum additional deformation of the spring in bringing the package to rest.