A nurse pushes a cart by exerting a force on the handle at a downward angle 35 degrees below the horizontal. The loaded cart has a mass of 28.0 kg, and the force of friction is 60.0N. What force must the nurse exert to move at a constant velocity?
in the horizontal:
force-forcefriction=0
Force*cos35=60
solve for force.
73.2N
52.58
A nurse pushes a cart by exerting a force on the handle at a downward angle 33.5° below the horizontal. The loaded cart has a mass of 29.5 kg, and the force of friction is 58.0 N.
To determine the force that the nurse must exert to move the cart at a constant velocity, we need to use Newton's second law of motion. Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the acceleration is zero since the cart is moving at a constant velocity.
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 ≈ 72.74 N
Therefore, the nurse must exert approximately 72.74 N of force to move the cart at a constant velocity.