The coefficient of static friction between a block and a horizontal floor is 0.40, while the coefficient of kinetic friction is 0.15. The mass of the block is 5.0 kg. A horizontal force is applied to the block and slowly increased. (a) What is the value of the applied horizontal force at the instant that the block starts to slide? (b) What is the net force on the block after it starts to slide?

Wb = mg = 5kg * 9.8N/kg = 49 N. = Wt. of block.

Fb = 49N @ 0 Deg.
Fp = 49*sin(0) = 0 = Force parallel to
floor.
Fv = 49*cos(0) = 49 N. = Force perpendicular to floor.

a. Fn = Fap - Fp - 0.4Fv = 0.
Fap - 0 - 19.6 = 0.
Fap = 19.6 N.

b. Fn = Fap - Fp - 0.15Fv.
Fn = 19.6 - 0 - 7.35 = 12.25 N.

Why did the block go to therapy? Because its static friction coefficient had commitment issues!

(a) To find the value of the applied horizontal force at the instant that the block starts to slide, we need to compare the maximum static friction force with the applied force. The maximum static friction force can be calculated by multiplying the coefficient of static friction (0.40) with the normal force (which is equal to the weight of the block, mg). So, maximum static friction force = 0.40 * 5.0 kg * 9.8 m/s^2 (acceleration due to gravity). Once the applied force exceeds this maximum static friction force, the block will start to slide.

(b) After the block starts to slide, we're dealing with kinetic friction. The force of kinetic friction can be calculated by multiplying the coefficient of kinetic friction (0.15) with the normal force (which is once again equal to the weight of the block, mg). So, force of kinetic friction = 0.15 * 5.0 kg * 9.8 m/s^2.

The net force on the block after it starts to slide is the difference between the applied force and the force of kinetic friction. Net force = applied force - force of kinetic friction.

To find the value of the applied horizontal force at the instant that the block starts to slide, we need to compare the force of static friction to the maximum force it can hold. The force of static friction is given by:

F_static = μ_static * N

where μ_static is the coefficient of static friction and N is the normal force (equal to the weight of the object, mg).

Given that μ_static = 0.40 and m = 5.0 kg, we can calculate the force of static friction:

F_static = 0.40 * 5.0 kg * 9.8 m/s² (using g = 9.8 m/s²)

F_static = 19.6 N

Therefore, at the instant the block starts to slide, the applied horizontal force is equal to the force of static friction: F_applied = 19.6 N.

Now, to calculate the net force on the block after it starts to slide, we need to consider the force of kinetic friction.

The force of kinetic friction is given by:

F_kinetic = μ_kinetic * N

where μ_kinetic is the coefficient of kinetic friction.

Given that μ_kinetic = 0.15 and m = 5.0 kg, we can calculate the force of kinetic friction:

F_kinetic = 0.15 * 5.0 kg * 9.8 m/s² (using g = 9.8 m/s²)

F_kinetic = 7.35 N

Since the block is sliding, the applied force is greater than the force of kinetic friction. Therefore, the net force on the block after it starts to slide is equal to the difference between the applied force and the force of kinetic friction:

Net Force = F_applied - F_kinetic = 19.6 N - 7.35 N = 12.25 N.

So, the net force on the block after it starts to slide is 12.25 N.

To find the answers to these questions, we need to use the concepts of static and kinetic friction and understand the forces acting on the block.

(a) To determine the value of the applied horizontal force at the instant the block starts to slide, we need to consider the static friction. The maximum static friction force is given by the equation:

F_s = μ_s * N

Where F_s represents the static friction force, μ_s is the coefficient of static friction, and N is the normal force acting on the block. The normal force N is equal to the weight of the block, which can be calculated as:

N = m * g

Where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s²).

Substituting the values, we have:

N = 5.0 kg * 9.8 m/s² = 49 N

Then we can calculate the maximum static friction force:

F_s = 0.40 * 49 N = 19.6 N

So, the value of the applied horizontal force at the instant the block starts to slide is approximately 19.6 Newtons.

(b) Once the block starts to slide, the friction changes from static to kinetic friction. The kinetic friction force is given by:

F_k = μ_k * N

Where F_k represents the kinetic friction force and μ_k is the coefficient of kinetic friction.

Substituting the values, we have:

F_k = 0.15 * 49 N = 7.35 N

The net force on the block after it starts to slide is the difference between the applied force and the kinetic friction force:

Net force = Applied force - Kinetic friction force

So, the net force on the block after it starts to slide is the value of the applied force minus 7.35 Newtons.