Question

A person pushes a 24.2-kg shopping cart at a constant velocity for a distance of 17.6 m on a flat horizontal surface. She pushes in a direction 22.7 ° below the horizontal. A 42.4-N frictional force opposes the motion of the cart. (a) What is the magnitude of the force that the shopper exerts? Determine the work done by (b) the pushing force, (c) the frictional force, and (d) the gravitational force.

Answer 1

(a)

Apply Newton's second law of motion, Net force is,

               ΣF = F cos17.6 - f = 0

               F cos17.6 - f = 0

                             F   = f / cos17.6

=42.4/0.9532

                     F_shopper= 44.48 N

(b)

Work done by the pushing force is,

W1 = Fd cos17.6

                  = (42.4)(17.6)( cos17.6 )

                   ≈ 711 J

(c)

Work done by frictional force is,

W = fd Cos180

                = (42.4)(17.6)(-1)

                = - 746.24 J

(d)

Work done by Gravity is,

W_g = Fd cos90

                   = (mg)(0)

                   = 0 J

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