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kc0ldeah
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Homework Statement
A crate of mass 10.0 kg is pulled up a rough incline with an initial speed of 1.5 m/s. The pulling force is 100 N parallel to the incline which makes an angle of 20.0° with the horizontal. The coefficient of kinetic friction is .4 and the cart is pulled 5.00 m.
e) What is the speed of the crate after being pulled 5.00m?
Homework Equations
Delta Energy Mechanical = -Force_friction(d) + Work_external
K_f + U_f = K_i + U_i - Force_friction(d) + Work_external
For constant Force and parallel force and displacement: W = F(d)
The Attempt at a Solution
K_f + U_f = K_i + U_i - Force_friction(d) + Work_external
.5mvf2 + mgh = .5mvi2 + 0 - Force_friction(d) + Work_external
h = 5sin(20°)
Force_friction = -μ Fn
= -μ 98cos(20°)
Work External = F(d) = 100N * 5m = 500J
.5mvf2 + mgh = .5mvi2 +μ 98cos(20°)(5) + 500
vf2 = (.5mvi2 +μ 98cos(20°)(5) + 500 - mgh) / (.5m)
v = 10.27 m/s
The answer is given as 5.65 m/s.
Any help is appreciated!
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