You want to nail a 1.5 kg board onto the wall of a barn. To position the board before nailing, you push it against the wall with a horizontal force F to keep it from sliding to the ground.

Question

You want to nail a 1.5 kg board onto the wall of a barn. To position the board before nailing, you push it against the wall with a horizontal force F to keep it from sliding to the ground.

(a) If the coefficient of static friction between the board and the wall is 0.71, what is the least force you can apply and still hold the board in place? N
(b) What happens to the force of static friction if you push against the wall with a force greater than that found in part (a)?

stays the same
decreases
increases

Answer 1

use the equation

x=mg/usk
so it will be(1.5)(9.8)/.71 for part a

part b i have no idea

Answer 2

To find the least force you can apply to hold the board in place, we need to consider the concept of static friction. Static friction is the force that resists the motion between two surfaces in contact, when there is no relative motion between them.

(a) To determine the least force required to hold the board in place, we need to find the maximum static friction force. The maximum static friction force can be calculated by multiplying the coefficient of static friction (μ_s) by the normal force (N) exerted on the object.
Formula: Friction force (f_s) = μ_s * N

In this case, the normal force exerted on the board in the vertical direction is equal to its weight, which can be calculated by multiplying the mass of the board (m) by the acceleration due to gravity (g).
Formula: Normal force (N) = m * g

Given:
Mass of the board (m) = 1.5 kg
Coefficient of static friction (μ_s) = 0.71
Acceleration due to gravity (g) = 9.8 m/s^2

Substituting the values into the formulas, we have:
Normal force (N) = 1.5 kg * 9.8 m/s^2 = 14.7 N
Friction force (f_s) = 0.71 * 14.7 N = 10.437 N (rounding to three decimal places)

Therefore, the least force you can apply and still hold the board in place is approximately 10.437 N.

(b) If you push against the wall with a force greater than the force found in part (a), the force of static friction between the board and the wall will increase. This is because the maximum static friction force depends on the coefficient of static friction and the normal force, not the applied force. As long as the applied force does not exceed the maximum static friction force, the force of static friction will adjust to match the applied force and prevent motion.