What force must be applied to push a carton weighing 350 N up a 19° incline, if the coefficient of kinetic friction is 0.45? Assume the force is applied parallel to the incline and the velocity is constant. (Enter the magnitude of the force.)
If the carton is moved at uniform velocity ma=0
F-F(fr) –mgsinα = 0
F= F(fr) +mgsinα =μmgcosα+ mgsinα =
=mg (μ•cosα + sinα)
To determine the force that must be applied to push the carton up the incline, we need to consider the forces involved.
First, let's determine the force of gravity acting on the carton. The force of gravity can be calculated using the formula:
force of gravity = mass * acceleration due to gravity
Since we are given the weight of the carton, we can calculate its mass using the formula:
weight = mass * acceleration due to gravity
350 N = mass * 9.8 m/s^2
Solving for the mass:
mass = 350 N / 9.8 m/s^2 ≈ 35.71 kg
Next, let's determine the force of friction acting on the carton. The force of friction can be calculated using the formula:
force of friction = coefficient of friction * force perpendicular to the surface
The force perpendicular to the surface can be calculated using the formula:
force perpendicular = weight * cos(angle of incline)
force perpendicular = 350 N * cos(19°)
Now, we can calculate the force of friction:
force of friction = 0.45 * force perpendicular
force of friction = 0.45 * (350 N * cos(19°))
Finally, the force required to push the carton up the incline is the sum of the force of gravity and the force of friction in the opposite direction. Since the velocity is constant, the net force is zero.
force applied - force of gravity - force of friction = 0
force applied = force of gravity + force of friction
force applied = mass * acceleration due to gravity + force of friction
Substituting the values:
force applied = (35.71 kg * 9.8 m/s^2) + (0.45 * 350 N * cos(19°))
Evaluating the expression:
force applied ≈ 35.71 kg * 9.8 m/s^2 + 0.45 * 350 N * cos(19°)
force applied ≈ 350.67 N
Therefore, the magnitude of the force that must be applied to push the carton up the incline is approximately 350.67 N.