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Energy in Physics!?
A cookie jar is moving up a 20° incline. At a point 55 cm from the bottom of the incline (measured along the incline), the jar has a speed of 1.4 m/s. The coefficient of kinetic friction between jar and incline is 0.20. (Use energy principles)
(a) How much farther up the incline will the jar move?
(b) How fast will it be going when it has slid back to the bottom of the incline?
Please, explain too!
THANKS!
1 Answer
- 1 decade agoFavorite Answer
Start by drawing a free body diagram.
Conservation of energy shows
a) Loss of Kinetic Energy = Gain in Potential Energy + Loss of Frictional Energy
½ mv^2 = mgh + uNx
Where:
m = mass
g = acceleration to gravity (9.8m/s^2)
h = height
N = normal force
x = distance traveled along the line
v = velocity
From the free body diagram it can be shown the N = mg cos 20, and h = x sin 20
Substituting into the equation
½ mv^2 = mgx sin 20 + umgx cos 20
Divide both sides by m
½ v^2 = gx sin 20 + ugx cos 20
Insert the given values
½ * 1.4^2 = 9.8 * 0.34 * x + .2 * 9.8 * .94 * x
0.98 = 3.332x + 1.8424x
0.98 = 5.174x
x = 0.189 (Meters) = the jar will move another 189 cm
b) Loss of Potential Energy = Gain of Kinetic Energy + Loss of Frictional Energy
mgh = ½ mv^2 + uNx (x = 189 + 55 = 244 cm = 0.244 m)
mgx sin 20 = ½ mv^2 + umgx cos 20
Divide both sides by m
gx sin 20 = ½ v^2 + ugx cos 20
Insert the given values
9.8 * 0.244 * 0.34 = ½ v^2 + 0.2* 9.8 * 0.244 * .94
0.831 = ½ v^2 + 0.45
v^2 = 0.762
v = 0.873 m/s when the jar has slid back to the bottom
