Velocity Of Load Up An Inclined Plane
Strings (SiPjAjk) = S7P3A31 Base Sequence = 12735 String Sequence = 12735 - 5 - 51
A cable exerts a constant force of 600 lbs to pull a 1000 lb load up a 2-degree inclined plane. How fast will the load be moving up the inclined plane 10 secs after the pull is applied if the coefficient of friction μ, between the load and the plane is 0.5.
(a) S7P5A51 (Physical Change - Velocity).
Pj Problem of interest is of type chnage. Problems of speed, velocity, acceleration, time (duration) are change problems.
Consider the above diagram (fig. 3):
The resultant force R, that caused the pull up the plane is calculated as follows:
R = forcing action on load - force resisting motion of load.
R = 600 - W(μcosθ + sinθ)
So, R = 600 - 1000(0.5cos2o + sin2o)
So, R = 600 - 535 = 65 lbs.
Next we use the impulse momentum, Rt to calculate velocity.
So, Rt = (W/g)[vf - vo].
Where W/g is mass of load; vf is velocity after 10 secs; and vo is velocity just before pull is applied.
So, 65 x 10 = (1000/32)[vf - 0].
So, vf = 20.9 ft/sec.
So, load is moving at 20.9 ft/sec up the inclined plane 10 secs after the pull is applied.
The point "." is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
Ordinary Differential Equations (ODEs)