A 10 kg penguin slips down a rough incline of 35o

. If the coefficient of kinetic friction
between the penguin and the incline is 0.15, determine the penguin’s acceleration.

net force down plane=ma

mgSinTheta-mg*mu*CosTheta=ma
solve for acceleration a.

To determine the penguin's acceleration, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

First, let's find the net force acting on the penguin. The net force is the vector sum of all the forces acting on the penguin.

The force of gravity is acting vertically downward with a magnitude of mg, where m is the mass of the penguin and g is the acceleration due to gravity (9.8 m/s^2).

The force of friction opposes the motion of the penguin and can be calculated using the equation: fr = μ * N, where μ is the coefficient of kinetic friction and N is the normal force acting perpendicular to the incline.

The normal force can be calculated as N = mg * cos(θ), where θ is the angle of the incline.

The force parallel to the incline can be calculated as F_parallel = mg * sin(θ).

Since the penguin is slipping down the incline, the force of friction opposes the motion and acts in the opposite direction of the force parallel to the incline. Therefore, the net force is given by:

Net force = F_parallel - fr.

Now, we can use Newton's second law to find the acceleration:

Net force = mass * acceleration.

Substituting the values, we get:

mg * sin(θ) - μ * (mg * cos(θ)) = mass * acceleration.

Plugging in the known values:

mass = 10 kg,
θ = 35 degrees,
μ = 0.15,
g = 9.8 m/s^2,

we can solve for the acceleration.

Using a scientific calculator or online trigonometric calculator, calculate sin(θ) and cos(θ). Substitute these values into the equation.

Finally, solve for acceleration.

Accelerations = (mg * sin(θ) - μ * (mg * cos(θ))) / mass.

Substituting the given values:

Acceleration = (10 kg * 9.8 m/s^2 * sin(35°) - 0.15 * (10 kg * 9.8 m/s^2 * cos(35°))) / 10 kg.

Calculating this expression will give you the penguin's acceleration.