Question

Consider an object on an incline where friction is present. The angle between the incline and the horizontal is θ and the coefficient of kinetic friction is μk.

Calculate the acceleration, in meters per second squared, of this object if θ = 33° and μk = 0.31. Treat down the incline as the positive direction.

Answer 1

The acceleration of the object on the incline is approximately 4.94 m/s².

Step-by-step explanation:

To calculate the acceleration of an object on an inclined plane with friction, we need to consider the forces acting on the object.

In this case, the force of gravity can be divided into two components: one parallel to the incline and one perpendicular to the incline.

When an object is on an incline with friction present, its acceleration can be calculated using the formula: a = g(sinθ - μkcosθ).

Where

a represents the acceleration

g is the acceleration due to gravity (approximately 9.8 m/s²)

θ is the angle between the incline and the horizontal (given as 33°)

μk is the coefficient of kinetic friction (given as 0.31).

Plugging in the given values, we have:

a = 9.8(m/s²) * (sin33° - 0.31cos33°)

a = 4.94 m/s².

So therefore the acceleration of the object on the incline is approximately 4.94 m/s².