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.

This solution contains step-by-step calculations to determine force applied to the ramp, coefficient of kinetic friction and velocity of object after the plane. All workings and formulas are shown with brief explanations.

(See attached file for full problem description with diagram and equations)
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The acceleration of a block of mass that is pulled up a frictionless plane inclined at angle with respect to the horizontal by a perfect string that passes over a perfect pulley to a block of mass that is hanging vertically.
Visualize th

1) a) Find the angle required to maximize the range down an incline which is pitched at an angle of −θ with respect to the horizontal and the projectile is shot an angle of φ above the incline at a speed of v0 .
b) Determine the distance down the incline at the angle found in a).
c) Plot the trajectory gi

1. A light horizontal spring has a force constant of k=100 N/m. A 2.00 kg block is pressed against one end of the spring, compressing it 0.100 m. When the block is released from rest it moves 0.250 m to the right of release position. Show that the coefficient of kinetic friction between the block and the horizontal surface is

A crate is resting on a ramp that is inclined at an angle above the horizontal. As it increased, the crate remains in place until it reaches a value of 29.2°. Then the crate begins to slide down the slope.
(a) Determine the coefficient of static friction between the crate and the ramp surface.
(b) The coefficient of kinet

Southern Air is considering purchase of new aircraft and has set aside $1.5B dollars for this.
They have enough pilots to crew 30 new planesand enough maintence personnel to crew
40 new short range planes.
Maint for long range planes is 1.67 times
that for short range planes
Maint for med range planes is 1.33 times
th

(See attached file for full problem description with diagram)
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A block with mass is placed on an inclined plane with slope angle and is connected to a second hanging block that has mass by a cord passing over a small, frictionless pulley. The coefficient of static friction is and the coefficient of kinetic friction is

Three objects are connected on an inclined table as shown in the diagram below. The objects have masses 8.0 kg, 4.0 kg and 2.0 kg as shown, and the pulleys are frictionless. The tabletop is rough, with a coefficient of kinetic friction of 0.47, and makes an angle of 20.0° with the horizontal.
a.free body diagram
b. Determ

A crate is resting on a ramp that is inclined at an angle 0(thada) the horizontal.As 0(thada) is increased, the crate remains in place until 0(thada)reaches a value of 38.0 degrees. Then the crate begins to slide down the slope. (a) Determine the coefficient of static friction between the crate and the ramp surface. (b) The coef

Please see attachment. Require problems solving, also explanations etc for better understanding of vectors.
VECTOR PROBLEMS
(1) Let l be the line with equation v = a + t u.
Show that the shortest distance from the origin to l can be written | a × u |