A grocery cart with mass of 14 kg is being pushed at constant speed up a 12 ramp

Question

A grocery cart with mass of 14 kg is being pushed at constant speed up a 12 ramp by a force FP which acts at an angle of 17 below the horizontal.

Part A

Find the work done by the force F P on the cart if the ramp is 6.5 m long.

Express your answer to two significant figures and include the appropriate units.

Part B

Find the work done by the force mg on the cart.

Express your answer to two significant figures and include the appropriate units.

Part C

Find the work done by the force F N on the cart.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

work done by a force W = F*s*costheta

F = force acting

s = displacement

theta = angle between s and F

at constant speed acceleration a = 0

along the incline

Fnet = m*a

mg*sin12 - F*cos17 = 0

F*cos17 = m*g*sin12 = 14*9.8*sin12 = 28.5 N

part A

work = F*cos17*S = 28.5*6.5 = 185.25 J <-------------ANSWER

part B

gravitational force acts down the incline

Wgravity = m*g*sintheta*s*cos180

Wgravity = -14*9.8*sin12*6.5 = -185.25 J <-------------ANSWER

part C

normal force is perpendicular to s

WN = Fn*s*cos90 = 0    <<<-------------ANSWER

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