A pig slides down a 29° incline in twice the time it would take to slide down a frictionless 29° incline. What is the coefficient of kinetic friction between the pig and the incline?

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calculation on physic: a tractor of mass 5.0×10^3kg is used to tow a car of mass 2.5×10^3kg. the tractor moved with a speed of 3.0m/s just before the towing rope becomes taut. calculate the speed of the tractor immediately the rope becomes taut?

To find the coefficient of kinetic friction between the pig and the incline, we can use the concept of time. First, we need to understand the principles involved.

When there is no friction, the time taken for an object to slide down an incline is solely dependent on the angle of the incline and the acceleration due to gravity. In this case, we'll call this time T.

When there is friction, the time it takes for the pig to slide down the incline will be longer than T, due to the opposing force of friction. Let's call this time 2T.

Now, let's start solving the problem step by step:

Step 1: Find the time it takes for the pig to slide down the frictionless incline, denoted as T.

Since the time for a frictionless incline is solely dependent on the angle, we can use one of the kinematic equations:

cos(angle) = acceleration due to gravity / (acceleration due to gravity * T)
1 = T * acceleration due to gravity / (acceleration due to gravity * T)

Canceling out the acceleration due to gravity and T, we get:
1 = 1

This equation tells us that the time for the frictionless incline is 1.

Step 2: Find the time it takes for the pig to slide down the incline with friction, denoted as 2T.

From the problem statement, we know that the time to slide down with friction is twice the time for the frictionless case:
2T = 2 * 1
2T = 2

Step 3: Calculate the coefficient of kinetic friction.

The time it takes for an object to slide down an inclined plane with friction is given as:

2T = (2 * pi * mass * sin(angle)) / (coefficient of kinetic friction * gravity)

Rearranging the equation:
(coefficient of kinetic friction * gravity) = (2 * pi * mass * sin(angle)) / 2T

Substituting the known values:
(coefficient of kinetic friction * gravity) = (2 * pi * mass * sin(29°)) / 2

Rearranging further and substituting the value of gravity (9.8 m/s²):
coefficient of kinetic friction = ((2 * pi * mass * sin(29°)) / 2) / (9.8 m/s²)

Now, input the known values of mass and the coefficients of sin(29°) to find the final answer.