The person in the drawing is standing on crutches. Assume that the force exerted on each crutch by the ground is directed along the crutch, as the force vectors in the drawing indicate. If the coefficient of static friction between a crutch and the ground is 1.12, determine the largest angle θMAX that the crutch can have just before it begins to slip on the floor.

I wasn't able to copy the picture too. So just use your imagination! Tried this one for at least 45 minutes!!

Two components of the force F:

F⒳= Fsinθ = F(fr)
F⒴ = Fcosθ= N
F(fr) = μN
Fsinθ =μFcosθ
tanθ=μ=1.12
θ=arctan1.12=48.24°

Wrong

To determine the largest angle θMAX that the crutch can have just before it begins to slip on the floor, we can analyze the forces acting on the crutch.

Let's assume that the crutch is at an angle θ with respect to the horizontal, and the force exerted on each crutch by the ground is directed along the crutch.

The forces acting on the crutch are:

1. The weight of the person, acting downward.

2. The normal force, acting perpendicular to the ground.

3. The static friction force, acting parallel to the ground.

To begin analyzing the forces, we need to break down the weight of the person into its components. The vertical component of the weight is balanced by the normal force, while the horizontal component contributes to the static friction force.

Let's denote the weight of the person as mg, where m is the person's mass and g is the acceleration due to gravity.

The vertical component of the weight is m*g*cos(θ), and it is balanced by the normal force.

The horizontal component of the weight is m*g*sin(θ), and it contributes to the static friction force.

The maximum static friction force can be calculated using the equation:

F(friction) = μ(static) * N

Where μ(static) is the coefficient of static friction and N is the normal force.

So, the maximum static friction force is μ(static) * m*g*cos(θ).

For the crutch to be on the verge of slipping, the maximum static friction force should equal the horizontal component of the weight.

Therefore, we have:

μ(static) * m * g * cos(θ) = m * g * sin(θ)

Cancelling out the mass and acceleration due to gravity:

μ(static) * cos(θ) = sin(θ)

We can rearrange this equation to solve for the angle θ:

μ(static) = tan(θ)

Taking the inverse tangent (arctan) of both sides:

θMAX = arctan(μ(static))

Now, substitute the given coefficient of static friction of 1.12 into the equation:

θMAX = arctan(1.12)

Using a scientific calculator or trigonometric table, the arctan(1.12) is approximately 47.18 degrees.

Therefore, the largest angle θMAX that the crutch can have just before it begins to slip on the floor is approximately 47.18 degrees.

To determine the largest angle θMAX that the crutch can have just before it begins to slip on the floor, we need to consider the forces acting on the crutch and analyze its equilibrium.

Here are the steps to find the maximum angle:

1. Identify the forces acting on the crutch:
- The weight of the person acting downward (W).
- The normal force from the ground acting upward, perpendicular to the ground (N).
- The static friction force between the crutch and the ground, which has a maximum value (Fs).

2. Determine the forces' components:
- Resolve the weight force into two components: one parallel to the crutch (W⊥) and one perpendicular to the crutch (W⊥).
- The normal force (N) has only a vertical component (N⊥).
- The static friction force (Fs) also has a vertical component (Fs⊥) and a parallel component (Fs∥).

3. Set up the equilibrium equations:
- In the vertical direction, the sum of vertical forces must be zero: N⊥ + W⊥ - Fs⊥ = 0.
- In the horizontal direction, there should be no net force: Fs∥ = 0.

4. Determine the maximum static friction:
- The maximum static friction (Fs MAX) can be calculated using the equation: Fs MAX = μsN⊥, where μs is the coefficient of static friction.

5. Calculate the largest angle θMAX:
- Using trigonometry, we have: tan θMAX = W⊥ / N⊥.
- Substitute the values of W⊥ and N⊥ obtained from step 2 into the equation.
- Solve for θMAX using the inverse tangent function: θMAX = tan^(-1) (W⊥ / N⊥).

It's important to note that without the specific values of the weight (W), the normal force (N), and the angle θ, we can only provide a general explanation of the steps to find θMAX. You'll need to use the given values in your problem to calculate the specific angle.