A factory worker pushes a 30.7 crate a distance of 4.0 along a level floor at constant velocity by pushing downward at an angle of 31 below the horizontal. The coefficient of kinetic friction between the crate and floor is 0.26.
What magnitude of force must the worker apply to move the crate at constant velocity?
downward? that means he is increasing friction.
Friction force=mu(mg+Force*Sin31)
horizontal force=force*cos31
set them equal, solve for force.
bob is correct, except that you have to subtract the Force*sin(31). It's a poorly worded problem, to say the least.
Bajs i skärten
To find the magnitude of force that the worker must apply to move the crate at constant velocity, we need to consider the forces acting on the crate.
First, let's determine the normal force (N) exerted by the floor on the crate. The normal force is equal in magnitude and opposite in direction to the force exerted by the crate on the floor. In this case, the force exerted by the crate on the floor is the result of the downward component of the worker's force.
Given that the worker is pushing downward at an angle of 31° below the horizontal, the downward force exerted by the worker can be determined using trigonometry:
Force_down = Force_applied * cos(31°).
Next, let's determine the force of kinetic friction (F_kinetic) acting on the crate. The force of kinetic friction can be calculated using the coefficient of kinetic friction (μ_kinetic) and the normal force (N):
F_kinetic = μ_kinetic * N.
Finally, in order to maintain constant velocity, the horizontal component of the worker's force must balance the force of kinetic friction. The horizontal component can be determined using trigonometry as well:
Force_horizontal = Force_applied * sin(31°).
Therefore, we can set up an equation for the forces:
Force_horizontal = F_kinetic,
Force_applied * sin(31°) = μ_kinetic * N.
Since N is equal to the weight of the crate (mg), we can write:
Force_applied * sin(31°) = μ_kinetic * mg.
Now, we can rearrange the equation to solve for the magnitude of the force applied (Force_applied):
Force_applied = (μ_kinetic * mg) / sin(31°).
Substituting the given values:
μ_kinetic = 0.26,
m = 30.7 kg,
g ≈ 9.81 m/s²,
Force_applied = (0.26 * 30.7 kg * 9.81 m/s²) / sin(31°).
Evaluating this expression, we find that the magnitude of the force the worker must apply to move the crate at constant velocity is approximately 161.6 N.