A 10.0 kg object is resting on a horizontal surface with a coefficient of friction of 0.7. Determine the minimum force that can move the object.At what inclination should force be applied?

M*g = 10 * 9.8 = 98 N. = Wt. of object = Normal(Fn).

Fs = u*Fn = 0.7 * 98 = 6.86 N. = Force of static friction.

F-Fs = M*a.
F-6.86 = 10*0 = 0.
F = 6.86 N.

Angle = 0o(parallel to the surface).

To determine the minimum force required to move the object, we need to consider the force of friction acting on it. The force of friction can be calculated using the formula:

Frictional force (Ff) = coefficient of friction (μ) * normal force

The normal force, in this case, is equal to the weight of the object, which can be calculated using the formula:

Weight (W) = mass (m) * acceleration due to gravity (g)

Substituting the given values, we find:

Weight (W) = 10.0 kg * 9.8 m/s^2 ≈ 98 N

Now, calculating the frictional force:

Ff = 0.7 * 98 N ≈ 68.6 N

The minimum force required to overcome the force of friction and move the object is equal to the force of friction itself. Therefore, the minimum force required to move the object is approximately 68.6 N.

To determine the inclination at which the force should be applied, we need to consider the relationship between the force applied, the component of the weight acting along the inclined plane, and the force of friction. The force applied can be resolved into two components: the force acting perpendicular to the inclined plane, and the force acting parallel to the inclined plane.

The component of the weight acting along the inclined plane can be calculated using the formula:

Weight component along the inclined plane = Weight * sin(θ)

Where θ is the angle of inclination.

Since the object is in equilibrium on the horizontal surface, the force of friction is equal to the force acting parallel to the inclined plane. So, the force applied must be larger than the force of friction. Mathematically, we can express this as:

Force applied > Force of friction

By substituting the known values, we have:

Force applied > 68.6 N

Hence, the force applied needs to be greater than 68.6 N for the object to move.

The inclination at which the force should be applied can be calculated using the formula:

θ = arcsin(Ff / Weight)

Substituting the known values, we find:

θ = arcsin(68.6 N / 98 N) ≈ 44.22 degrees

Therefore, the inclination at which the force should be applied is approximately 44 degrees.