Question

A nurse pushes a cart by exerting a force on the handle at a downward angle 35.0º 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

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

Step-by-step solution

Given data

• Angle below the horizontal = 35.0º.
• The loaded cart’s mass = 28.0 kg.

• the force of friction = 60.0 N.

(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.

(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:

$\begin{array}{c}\sum F_x=0\\ F\cos {35}^{°}-f=0\\ F=\frac{f}{\cos {35}^{°}}\end{array}$

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

$\begin{array}{c}F=\frac{60\text{\hspace{0.33em}N}}{\cos {35}^{°}}\\ =\frac{60\text{\hspace{0.33em}N}}{0.819}\\ =73.26\text{\hspace{0.33em}N}\end{array}$

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