What minimum force is required to drag a crate (m = 40 kg) across a floor (co-efficient of kinetic friction = 0.6) if the force is applied at a 45 degree angle upward from the horizontal?
Help ASAP please!!
the force has an upward compnonet, which reduces weight.
fup=mg*sin45
So friction force then is
mu*mg(1-sin45)
so the horizontal component has to be equal to friction
Fcos45=mu*mg(1-sin45)
solve for F
What is the answer and how do you get that answer?
To determine the minimum force required to drag the crate across the floor, we need to consider the forces acting on the crate.
1. Weight force (mg): The weight force is the force due to the crate's mass and acts vertically downward. Its magnitude is given by the formula Fg = mg, where m is the mass of the crate (40 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. Normal force (N): The normal force is the force exerted by the surface on the crate, perpendicular to the floor. Since the crate is on a horizontal surface, the normal force is equal and opposite to the weight force, i.e., N = mg.
3. Frictional force (Ff): The force of friction opposes the motion of the crate and acts parallel to the floor. The magnitude of the frictional force is given by the equation Ff = μN, where μ is the coefficient of kinetic friction (0.6) and N is the normal force.
4. Applied force (F): This is the force that is being applied at a 45-degree angle upward from the horizontal (since it is not strictly horizontal). This force can be resolved into two components: one component that acts parallel to the floor (to overcome friction) and one component that acts vertically (to counteract weight).
To find the minimum force required, we need to find the component of the applied force parallel to the floor. Let's call it Fa.
Fa = F * cos(theta)
Where theta is the angle between the applied force and the horizontal (45 degrees in this case). Therefore:
Fa = F * cos(45 degrees)
Now, we can equate the force of friction and the parallel component of the applied force:
Ff = Fa
Substituting values, we have:
0.6N = F * cos(45 degrees)
Since N = mg, we can further simplify:
0.6 * (40 kg * 9.8 m/s^2) = F * cos(45 degrees)
Simplifying further:
F = (0.6 * (40 kg * 9.8 m/s^2)) / cos(45 degrees)
Therefore, the minimum force required to drag the crate is approximately the calculated value of F.