To use the principle of work and energy to determine characteristics of a mass b
ID: 1323928 • Letter: T
Question
To use the principle of work and energy to determine characteristics of a mass being pulled up an incline and determine the power that must be supplied to the system when the efficiency of the input system is considered.
As shown, a 56kg crate is pulled up a ? = 65? incline by a pulley and motor system. Initially at rest, the crate is pulleds = 4.5m up along the incline. Undergoing constant acceleration, the crate reaches a speed of 2.7m/s at the instant it has traveled this distance.
Part A - Power supplied to the crate when friction is considered
Considering the coefficient of kinetic friction, ?k = 0.15, determine the power that the motor must supply to the crate the instant the crate travels a distance of 4.5m .
Express your answer to two significant figures and include the appropriate units.
Part B - Power supplied to the motor when efficiency is considered
If the motor has an efficiency of ? = 0.87 , what power must be supplied to the motor to raise the crate?
Express your answer to two significant figures and include the appropriate units.
To use the principle of work and energy to determine characteristics of a mass being pulled up an incline and determine the power that must be supplied to the system when the efficiency of the input system is considered. As shown, a 56kg crate is pulled up a ? = 65? incline by a pulley and motor system. Initially at rest, the crate is pulleds = 4.5m up along the incline. Undergoing constant acceleration, the crate reaches a speed of 2.7m/s at the instant it has traveled this distance. Part A - Power supplied to the crate when friction is considered Considering the coefficient of kinetic friction, ?k = 0.15, determine the power that the motor must supply to the crate the instant the crate travels a distance of 4.5m . Express your answer to two significant figures and include the appropriate units. Part B - Power supplied to the motor when efficiency is considered If the motor has an efficiency of ? = 0.87 , what power must be supplied to the motor to raise the crate? Express your answer to two significant figures and include the appropriate units.Explanation / Answer
Using first equation of motion,
v = at
t = v/a
s = 1/2 a * t* t = 0.5*a*(v/a)*(v/a)
= 0.5*v^2/a
=>a = 0.5*v^2/s = 338/375= 0.81
Net forward force = ma = 56*a = 45.36 N
Friction force = u*Normal force = u*mg*cos65= 0.13**56*9.8*cos65= 30.151 N
Total backward force = friction + mgsin(65)= 30.151+56*9.8*sin(65)= 527.533 N
Total forward force = backward + net force = 527.533+45.36 = 572.893 N
A) Power supplied = force * velocity = 572.893* 2.7= 1.5 *10^3 W
B) Power supplied to motor = 1546.81/0.87= 1.8*10^3W
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