A person pushes a 18.8-kg shopping cart at a constant velocity for a distance of 17.9 m on a flat horizontal surface. She pushes in a direction 32.1 ° below the horizontal. A 52.7-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.

a) F = 62.2 N, b) W = 973.2 J, c) W = - 943.3 J and d) W = 0 J

Explanation:

Work is a scalar that is obtained from the scalar product of two vectors, force and displacement. the bold are vectors

W = F. d = F d cos θ

a) As the car travels at constant speed the acceleration is zero

Fx - fr = 0

Fx = fr

Cos θ = Fx / F

F cos θ = fr

F = fr / cos θ

F = 52.7 / cos 32.1

F = 62.2 N

Is the force exerted by the person

b) Let's calculate the thrust force jobs

W = 62.2 17.9 cos 32.1

W = 973.2 J

c) The force of friction that opposes the movement and is on the x-axis

W = fr d cos 180

W = 52.7 17.9 cos 180

W = - 943.3 J

d) The force of gravity that is vertical and has an angle of 90º with respect to the displacement

W = mg d cos 90

W = 0 J