Inclined Planes and Motion

46) A furniture crate of mass 60.8 kg is at rest on a loading ramp that makes an angle of 25.8 degrees with the horizontal. The coefficient of kinetic friction between the ramp and the crate is .272. What force, (in Newtons) applied parallel to the ramp, is required to push the crate up the incline at a constant speed?

47) A shopper pushes a 40.7-kg cart up a 23.1-degree smooth ramp, What force (in Newtons), directed along the incline, must the shopper exert to give the cart an acceleration of .726 m/s/s?

48) A box slides down a 33.1-degree ramp with an acceleration of 1.3 m/s/s. Determine the coefficient of kinetic friction between the box and the ramp. Enter your answer accurate to the fourth decimal place.

49) A box weighing 5544 N is being pulled up an inclined plane that rises 2.22 m for every 7.81 m of length measured along the incline. If the coefficient of friction is .599, determine the force (in Newtons), applied parallel to the incline, necessary to move it up the incline at constant speed.

50) A crate is held at rest on a frictionless 53.7-degree ramp by a rope parallel to the incline. If the tension in the rope is 7061 N, then what is the mass (in kg) of the crate?

51) A 40.6-kg wagon is towed up a hill which is inclined at 18.5 degree with respect to the horizontal. The tow rope is parallel to the incline and has a tension of 145 N in it. Assume that the wagon starts from rest at the bottom of the hill and neglect friction. How fast (in m/s) is the wagon going after moving 67.2-meters up the hill?

54) A 31.9-kg block starts from rest on the top of a 33.6-degree incline and slides a distance of 2.0 meters in 4.0 seconds. Determine the coefficient of friction between the block and the incline. Enter your answer accurate to the fourth decimal place.