in the horizontal:
force-forcefriction=0
Force*cos35=60
solve for force.
force-forcefriction=0
Force*cos35=60
solve for force.
First, we need to resolve the downward angle of 35 degrees into its vertical and horizontal components. The vertical component of the force is given by Fv = F * sin(theta), where F is the force exerted by the nurse and theta is the angle of 35 degrees. The horizontal component of the force is given by Fh = F * cos(theta).
Next, we need to calculate the gravitational force acting on the cart. The gravitational force is given by F_gravity = m * g, where m is the mass of the cart and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Since the cart is at a constant velocity, the force exerted by the nurse must balance out the force of friction. The force of friction is acting in the opposite direction of the nurse's force and has a magnitude of 60 N.
Setting up an equation with the horizontal components of the forces, we have:
Fh - F_friction = 0
Substituting Fh = F * cos(theta) and F_friction = 60 N, we can solve for F:
F * cos(theta) - 60 N = 0
Simplifying the equation, we have:
F * cos(35 degrees) = 60 N
Solving for F, we get:
F = 60 N / cos(35 degrees)
Calculating the value, we find:
F β 72.74 N
Therefore, the nurse must exert approximately 72.74 N of force to move the cart at a constant velocity.