1. Understand the Forces
* Weight (W): The force of gravity acting on the block. Its magnitude is 110 N.
* Normal Force (N): The force exerted by the incline on the block, perpendicular to the surface.
* Friction Force (f): The force that opposes the block's potential motion down the incline. It's static friction because the block is at rest.
* Component of Weight Parallel to the Incline (W_parallel): This is the component of the weight that pulls the block down the incline.
2. Free Body Diagram
Draw a free body diagram of the block, showing all the forces acting on it. This will help you visualize the problem.
3. Calculate the Components of Weight
* W_parallel = W * sin(θ)
* W = 110 N
* θ = 32°
* W_parallel = 110 N * sin(32°) ≈ 58.2 N
* W_perpendicular = W * cos(θ)
* W = 110 N
* θ = 32°
* W_perpendicular = 110 N * cos(32°) ≈ 93.4 N
4. Determine the Maximum Static Friction Force
* f_max = μ_s * N
* μ_s = 0.35 (coefficient of static friction)
* N = W_perpendicular ≈ 93.4 N
* f_max = 0.35 * 93.4 N ≈ 32.7 N
5. Compare the Forces
* The force pulling the block down the incline (W_parallel) is 58.2 N.
* The maximum static friction force (f_max) is 32.7 N.
Since the maximum static friction force is less than the component of weight pulling the block down, the block would slide down the incline if there were no other forces acting on it.
6. Force Due to Friction
Because the block is held motionless, the friction force is equal to the component of weight parallel to the incline:
* f = W_parallel = 58.2 N
Therefore, the force due to friction holding the block motionless is 58.2 N.
