# Homework Help: Contact force of block on a wall

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1. Apr 1, 2017

### dodosenpai

1. The problem statement, all variables and given/known data
In this sketch, the mass m = 1.6 kg is pushed against a wall by force F, as shown, in the horizontal direction. The values of the coefficients of kinetic and static friction for the contact between are 0.81 and 0.84 respectively. The magnitude of F is slowly and continuously reduced. Just before the block falls, what is the total contact force Fc exerted by the block on the wall. What is the magnitude of that force and what is the angle θ it makes with horizontal? (+ve for above, -ve for below the horizontal).

2. Relevant equations
Ff = μsN

3. The attempt at a solution

Since the block is not moving:
Input F = N
Ff = Fg

Therefore mg = μs*N

Rearrange we get

N = mg/μs
= (1.6*9.8)/0.84
= 18.66667
= 19(2 sig. fig.)

Since Input F = N, wouldn't the contact force of the mass onto the wall be 19N? Apparently this is wrong.

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2. Apr 1, 2017

### vela

Staff Emeritus
There are two forces the wall exerts on the block. The problem is asking for the sum of the normal force and the force of static friction.

3. Apr 1, 2017

### dodosenpai

So that would be that the contact force is not horizontal, but instead has a magnitude of √((0.84*19)2+(19)2) = 24.81 = 25N at an angle of tan-1(0.84) = 40.03 = 40°?

4. Apr 1, 2017

### dodosenpai

So that would be that the contact force is not horizontal, but instead has a magnitude of √((0.84*19)2+(19)2) = 24.81 = 25N at an angle of tan-1(0.84) = 40.03 = 40°?

5. Apr 1, 2017

### vela

Staff Emeritus
Yup, but I wouldn't use the rounded value for N in your calculations. Round to the correct number of sig figs only at the end of the calculation.

6. Apr 1, 2017

Thanks