To measure the static friction coefficient between a 1.6-kg block and a vertical wall, the setup shown in the drawing is used. A spring (spring constant = 400 N/m) is attached to the block. Someone pushes on the end of the spring in a direction perpendicular to the wall until the block does not slip downward. The spring in such a setup is compressed by 0.050 m. What is the coefficient of static friction?

F1 = m*g = 1.6kg * 9.8N/kg = 15.68 N

F2 = (0.05m/1m) * 400N = 20 N.

F1-Fs = m*a
15.68-Fs = m*0 = 0
Fs = 15.68 = Force of static friction.

Fs = u*F2 = 15.68
u*20 = 15.68
u = 0.784 = Coefficient of static friction.

Well, well, well! Looks like we've got a friction party going on here. Let me crunch some numbers for you!

We can start by finding the force exerted by the spring. Using Hooke's Law (F = kx), where F is the force, k is the spring constant, and x is the compression, we get:

F = (400 N/m) * (0.050 m) = 20 N

The force exerted by the spring should be equal to the maximum static friction force preventing the block from slipping downward. This maximum static friction force is given by:

f_s = μ_s * N

where f_s is the maximum static friction force, μ_s is the static friction coefficient, and N is the normal force.

Since the block is not moving downward, we have equilibrium. This means the weight of the block is balanced by the normal force:

N = mg

where m is the mass of the block and g is the acceleration due to gravity.

Substituting this into our maximum static friction force equation, we get:

f_s = μ_s * mg

Now, we need to find the normal force. Since the block is pressed against the wall, the normal force is equal to the perpendicular component of the weight:

N = mg * cos(90°) = 0

Well, well, well. That's quite a pickle! The normal force is zero. This can only mean one thing - the static friction force is also zero. If there's no friction, there's no coefficient of static friction to calculate. So, in this case, our coefficient of static friction is a whopping ZERO. Slip away, my friend, slip away!

To determine the coefficient of static friction between the block and the vertical wall, we can use the concept of equilibrium. When the block is not slipping downward, the forces acting on the block are balanced.

Let's break down the forces acting on the block:

1. Weight (mg): The weight of the block acts vertically downward and can be calculated as the product of the mass (m = 1.6 kg) and the acceleration due to gravity (g = 9.8 m/s^2). This force can be expressed as mg.

2. Normal force (N): The normal force acts perpendicular to the wall and supports the weight of the block. It is equal in magnitude and opposite in direction to the weight of the block. Therefore, the normal force can be expressed as mg.

3. Spring force (Fs): The spring force is exerted by the compressed spring and acts in the opposite direction to the displacement of the spring. The magnitude of the spring force can be calculated using Hooke's Law: Fs = k * x, where k is the spring constant (k = 400 N/m) and x is the displacement of the spring (x = 0.050 m).

4. Frictional force (f): The frictional force acts parallel to the wall and opposes the motion of the block. Since the block is not slipping downward, the frictional force will be static friction.

Now, we can set up an equation based on the equilibrium condition:

Sum of forces in the vertical direction = mg + N = 0
mg + mg = 0
2mg = 0

Since the sum of the forces in the vertical direction is zero, this tells us that the normal force is equal in magnitude to the weight of the block.

Sum of forces in the horizontal direction = Fs - f = 0
k * x - f = 0
400 N/m * 0.050 m - f = 0
20 N - f = 0
f = 20 N

The value of the frictional force (f) is 20 N. To find the coefficient of static friction (µ), we need to divide the frictional force by the normal force.

µ = f/N = 20 N / (mg) = 20 N / (1.6 kg * 9.8 m/s^2) ≈ 1.28

The coefficient of static friction between the block and the wall is approximately 1.28.

no <3

forrest's mama said life is like a box of chocolates. you never which physics problem youre gonna get. also me and forrest were like peas and carrots