How Does Friction Affect Motion in These Physics Problems?

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Friction plays a crucial role in determining the motion of objects in various physics problems. In the first scenario, a 2.5 kg block experiences a frictional force influenced by applied horizontal and vertical forces, with the static friction maximum calculated at 5.94 N. The second problem involves a person hanging from a rafter, where the gravitational force of 774.2 N and a static friction coefficient of 0.65 are used to find the normal force, but the initial calculation of 1191 N is incorrect. The third scenario describes a child sliding down a slope with a specific acceleration, prompting questions about determining the coefficient of kinetic friction. Overall, understanding the relationships between forces and friction is essential for solving these physics problems effectively.
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Homework Statement



A 2.5 kg block is initially at rest on a horizontal surface. A horizontal force F of magnitude 5.7 N and a vertical force P are then applied to the block. The coefficients of friction for the block and surface are s = 0.36 and k = 0.23.

Determine the magnitude of the frictional force acting on the block if the magnitude of P is 8.0 N.


Homework Equations



f = \mu Fn


The Attempt at a Solution



The force due to gravity is 2.5kg(9.8 m/s^2) = 24.5 N

The normal force would be 16.5 N.

The magnitude of the maximum value for the static frictional force is 5.94.

I do not know where to go from here.


Homework Statement



In about 1915, Henry Sincosky of Philadelphia suspended himself from a rafter by gripping the rafter with the thumb of each hand on one side and the fingers of the other side. Sincosky's mass was 79 kg. If the coefficient of static friction between hand and rafter was 0.65, what was the least magnitude of the normal force on the rafter from each thumb or opposite fingers? (After suspending himself, Sincosky chinned himself on the rafter and then moved hand-over-hand along the rafter. If you do not think Sincosky's grip was remarkable, try to repeat his stunt.)

This problem is very easy and I know that it is easy. I just can't seem to get the correct answer.

Homework Equations



He is hanging. The gravitational force is 79kg(9.8m/s^2) = 774.2 N and is parallel to the surface he is gripping. \mu = 0.65

The Attempt at a Solution



i did 774.2N = 0.65Fn. and got Fn = 1191 N which is incorrect.

Homework Statement



Playing near a road construction site, a child falls over a barrier and down onto a dirt slope that is angled downward at 30° to the horizontal. As the child slides down the slope, he has an acceleration that has a magnitude of 0.55 m/s2 up the slope. What is the coefficient of kinetic friction between the child and the slope?

This one I don't know where to start.
 
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I do not understand how can I solve the problem #2. I did drew free body diagram. It has gravitational force pointed down, normal force pointed up. Both forces are equal. Static fricition of 0.65 pointed up, am I right? Then, how can I find minimum normal force?
 
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