Push a Block against a Wall- Static Friction

Phoenixtears

1. The problem statement, all variables and given/known data

A 9 N horizontal force F pushes a block weighing 13.0 N against a vertical wall (Fig. 6-21). The coefficient of static friction between the wall and the block is 0.62, and the coefficient of kinetic friction is 0.42. Assume that the block is not moving initially.


(Image attached)

Determine the normal force that the wall exerts against the block
9 N (It is the same amount pushing against the block- they should be equal)

Determine the blocks acceleration
m/s^2


2. Relevant equations

Fk= (Coefficient of K)*N
F=ma
Max= Push- normal
May= Static- mg

3. The attempt at a solution

Alright, I began drawing a force graph. On this graph weight faces down, normal force is exerted left (see attachement), static force is exerted up, and push force is exerted right. Determining the acceleration means horizontally, because the acceleration vertically is 9.8. Now, looking at my equations, only one contains 'a': F=ma. So, what do I know in this equation? I can get mass from the 13 N weight. 13/9.8= 1.32653 mass. That just leaves me to find the force. Going back, the acceleration I am trying to find is horizontal. So, I need to use the push-normal to get my total force. Here's my big problem, don't the push force and the normal force equal each other? So that would leave me with an Ma= 0. What does this mean? What have I done wrong?

Thank you in advance!

~Phoenix

Attached Thumbnails

 

alphysicist

Hi Phoenixtears,

At this point I cannot view your attachment, but I can point out a couple of things about what you have written.

In the horizontal direction, if the two horizontal forces are equal and opposite, then they will give zero horizontal acceleration like you have found.

In the vertical direction, you seem to be assuming that the acceleration is 9.8m/s^2, which is not true. If an object is in free fall, its acceleration is 9.8m/s^2 downwards, but being in free fall means that gravity is the only force acting on it. However, here there are two forces in the vertical direction: gravity and the frictional force, so you have to use Newton's law to find out what the acceleration is.

t-money

Draw a free body diagram, if using the textbook knight. Otherwise draw a simple diagram and just as alphysicist suggested use Newtons Laws. You are asked for an acceleration but what direction is it in. Which way do you think it would go, imagine lightly holding a block up against a wall which way would it likely go?