Physics Problem - Work/Energy Theorem?
A 40.0 N crate starting at rest slides down a rough 6.0 m long ramp inclined at 30.0° with the horizontal. The force of friction between the crate and ramp is 6.0 N. Using the work-kinetic energy theorem, find the velocity of the crate at the bottom of the incline.
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Take g as 10 m/s^2, then mass of crate = 4 kg.
Potential energy lost at bottom of slope P = mgh = mgl sin(theta) = ... J
Frictional energy lost E = F x d = ... J
Net energy retained = K.E. = 0.5 mv^2 = P - E = ... J
v = sqrt ( 2(P - E) / m ) = ... m/s^2
120 J, 36 J, 84 J. 6.48 m/s^2
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The motion is anti-parallel to the friction. Work is just the integral of the dot product of the force and the infinitesimal displacement. The dot product of anti-parallel vectors is negative, so friction does negative work.