1: A plane is inclined at an angle of 30 deg. w/ respect to the horizon. A block of mass 6.0 kg is placed at the bottom of the plane and given an initial velocity of 3.0 m/sec up the plane. The coefficient of friction between the block and plane is 0.25.
a) How far up the plane will the block go?
b) Assuming the block slid

The velocity of a 1.9 kg block sliding down a frictionless inclinedplane is found to be 1.15 m/s. 1.40 s later, it has a velocity of 5.35 m/s. What is the angle of the plane with respect to the horizontal (in degrees)?

(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 planeinclined 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

A wood cylinder of mass m = .250 kg and length L=.100m, with N =10.0 turns of wire wrapped around it longitudinally, so that the plane of the wire coil contains the long central axis of the cylinder. The cylinder is released on a planeinclined at an angle theta to the horizontal, with the plane coil parallel to the incline plan

A 90g bullet is fired from a rifle having a barrel 0.690m long. Assuming the origin is placed the bullet begins to move, the force (in newtons) exerted on the bullet by the expanding gas is 1000 + 6000x- 35000x*x where x is in meters.
a) Determine the work done by the gas on the bullet as the bullet travels the length of the

The spring of a spring gun has force constant k = 400 N/m and negligible mass. The spring is compressed 6.00 cm and a ball with mass 0.0300 kg is placed in the horizontal barrel against the compressed spring. The spring is then released, and the ball is propelled out the barrel of the gun. The barrel is 6.00 cm long, so the ball

A hoop of radius 0.5 m and a mass of 0.2kg is released from rest and allowed to roll down an inclinedplane. How fast is it moving after being dropped from a vertical distance of 3m?
a. 5.4 m/s
b. 3.8 m/s
c. 7.7 m/s
d. 2.2 m/s

State all the assumptions and show all the work. Define your decision variables clearly. Briefly explain the constraints and objectives functions and define all unit of measure.
You have been put in charge of the Davidson oil refinery. The refinery produces gas and heating oil from crude oil. Gas sells for $11 per barrel and

(See attached file for full problem description with diagram)
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A block with mass is placed on an inclinedplane 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