1. A snowboarder of mass 60 kg is at rest on

the top of a sand dune. The coefficients of
static and kinetic friction are 0.55 and 0.4675,
respectively.

60 kg
μk = 0.4675
μs = 0.55

What is the angle � the incline must exceed
so that the snowboarder starts sliding? The
acceleration of gravity is 9.8 m/s2 .
Answer in units of ◦.

2. What is the acceleration down the incline if
� = 35 ◦, exceeding the value found in the
previous question?

Please help. I am so confused.

See previous post: Wed, 11-2-16, 8:37 PM.

To solve both of these questions, we need to use the concepts of friction and forces on inclined planes. Here's a step-by-step guide to solving each question:

1. Determining the angle of incline for the snowboarder to start sliding:
To start sliding, the force of friction needs to be overcome by the component of the force of gravity acting parallel to the incline. The force of friction can be calculated using the coefficient of static friction (μs) and the normal force (mass x gravity):

Frictional Force (Ff) = μs x Normal Force

The normal force can be found by decomposing the gravitational force into its components:

Normal Force (Fn) = mass x gravity x cos(θ)

where θ is the angle of the incline. The force component parallel to the incline is given by:

Parallel Force (Fp) = mass x gravity x sin(θ)

Equating the force of friction and the parallel force:

μs x Normal Force = Parallel Force

Solving for θ:

sin(θ) = μs x cos(θ)

Use the inverse sine function to find θ. The resulting value is the angle the incline must exceed for the snowboarder to start sliding.

2. Calculating the acceleration down the incline:
The acceleration down the incline can be found using the angle of incline (θ) and the coefficient of kinetic friction (μk). The force component parallel to the incline is given by:

Parallel Force (Fp) = mass x gravity x sin(θ)

The force of friction can be calculated using the coefficient of kinetic friction (μk) and the normal force (mass x gravity):

Frictional Force (Ff) = μk x Normal Force

The net force down the incline is given by:

Net Force (Fnet) = Fp - Ff

Finally, the acceleration down the incline can be found using Newton's second law:

Acceleration (a) = Fnet / mass

Substitute the values into the equations and calculate the acceleration. Note that the acceleration down the incline will vary based on the specific angle (θ) and the value of the coefficient of kinetic friction (μk).