Final answer:
To move the cart at a constant velocity, the nurse must exert a force that counteracts the force of friction. The force of friction is 60.0 N and must be overcome by the horizontal component of the nurse's applied force, calculated using trigonometry with the angle of 35° below the horizontal.
Step-by-step explanation:
The student's question involves a situation where a nurse needs to exert a force to move a cart with a mass of 28.0 kg at a constant velocity, considering frictional forces. To solve this, two steps are necessary: drawing a free-body diagram and calculating the required force.
Free-body Diagram
In the free-body diagram, the following forces are represented: the gravitational force (weight) acting downward, the normal force provided by the floor acting upward, the frictional force opposing motion, and the force exerted by the nurse at a downward 35.0° angle.
Calculating the Force
To move the cart at a constant velocity, the force exerted by the nurse must counteract the force of friction. The force of friction is given as 60.0 N, and this is the force that must be overcome horizontally. Since the force exerted by the nurse also has a vertical component due to being at an angle, it's necessary to use trigonometry to find the horizontal component of the applied force. The formula for this is Fapplied * cos(Θ) = frictional force, where Θ is the angle below the horizontal.
To find the force exerted by the nurse, we simply rearrange the formula to solve for Fapplied: Fapplied = frictional force / cos(35.0°). Using this equation, the nurse must exert a force of more than 60.0 N / cos(35.0°) to account for the downward angle and overcome the friction to move the cart at a constant velocity.