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Chapter 4: Q4.6-35PE (page 163)

A nurse pushes a cart by exerting a force on the handle at a downward angle 35.0潞 below the horizontal. The loaded cart has a mass of 28.0 kg, and the force of friction is 60.0 N.

(a) Draw a free-body diagram for the system of interest.

(b) What force must the nurse exert to move at a constant velocity?

Short Answer

Expert verified

(b) The force exerted by the nurse is 73.26 N.

Step by step solution

01

Given data

  • Angle below the horizontal = 35.0潞.
  • The loaded cart鈥檚 mass = 28.0 kg.
  • the force of friction = 60.0 N.
02

(a) The free-body diagram showing the forces involve

Here, F is the force exerted on the cart, f is the force of friction, and W is the weight of the cart.

03

(b) Determine the force exerted by the nurse on the cart

To move at a constant velocity, the sum of the forces in the x-direction must be zero as:

鈭�Fx=0Fcos35掳鈭�f=0F=fcos35掳

Substitute 60 N for f in the above expression, and we get,

F=60鈥凬cos35掳=60鈥凬0.819=73.26鈥凬

Hence, the force exerted by the nurse is 73.26 N.

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