you want to nail a 1.6 kg board onto the wall of a barn. to position the board before nailing, you push it against the wall with a horizontal force to keep it from sliding to the ground. (a) if the coefficient of static friction between the board and wall is .79, what is the least froce you can apply and still hold the board in place? (b) what hppens to the force of static friction if you push against the wall with a force greater that that found in part a?
OK so it's hard to draw a free-body diagram on a computer but it would be a the board with its weight(mg) pulling it down, the frictional force holding it up, the Normal force being one horizontal component, and the Force you're applying being the opposite horizontal component. Since the object is in equilibrium you can use the 2 equations
F(static)=weight(mg) and Normal=Force applied
and then the frictional force formula
F(static)=constant*Normal
so substituting equations,
F(static)=constant*Force applied
weight=constant*Force applied
Force applied=mg/constant
F applied=(1.6)(9.8)/.79=19.8N
and as you can see from the previous work, increasing the force applied increases the normal force which then increases the frictional force
Just tried it on my hw, and you do divide. Multiplying gave me the wrong answer.
(a) Well, well, well, it seems we have a board-nailing situation here! The coefficient of static friction between the board and the wall is a whopping 0.79. To find the least force needed to hold the board in place, we can utilize a simple formula.
Now, remember, my friend, that the force of static friction is directly proportional to the force pushing against it. So the least force you can apply to hold the board in place would be the same value as the force of static friction. Mathematically speaking, we can express this as:
Force of static friction (μ_s) = coefficient of static friction (0.79) * Normal force (mg)
Here, m is the mass of the board (1.6 kg) and g is the gravitational acceleration (approximately 9.8 m/s^2). So we plug in the numbers, do the math, and voila! You'll have your answer. Good luck holding that board in place!
(b) Ah, so you're feeling extra strong today, huh? If you push against the wall with a force greater than the one you found in part (a), well, let me tell you what happens to the force of static friction. Brace yourself!
The force of static friction will initially increase, keeping up with your mighty push. However, my dear friend, if you exceed a certain threshold, the force of static friction won't be able to handle your strength anymore. The board will suddenly start sliding down the wall, and the force of static friction will change into the force of kinetic friction.
So, to summarize, if you push with a force greater than what's needed to hold the board in place, you'll be in for a little surprise, as the board will start sliding down, and the force of static friction will no longer be able to save the day. Don't say I didn't warn you!
To find the least force you can apply to hold the board in place, you need to consider the maximum force of static friction between the board and the wall.
(a) The force of static friction (Fs) can be calculated using the equation Fs = μs * N, where μs is the coefficient of static friction and N is the normal force exerted on the board. In this case, the normal force is equal to the weight of the board, which can be found using the formula N = mg, where m is the mass of the board (1.6 kg) and g is the acceleration due to gravity (9.8 m/s^2).
Substituting these values into the equation, we get Fs = 0.79 * (1.6 kg * 9.8 m/s^2) = 12.47 N.
Therefore, the least force you can apply to hold the board in place is 12.47 N.
(b) If you push against the wall with a force greater than 12.47 N, the board will not move horizontally but will experience kinetic friction instead of static friction. The force of static friction can only counteract forces up to a certain limit, known as the maximum static friction. Once this limit is exceeded, the static friction is overcome, and the object starts to slide.
Therefore, if you exert a force greater than the maximum static friction, the board will start sliding down the wall, and the force of static friction will be replaced by the force of kinetic friction.