A slide loving pig slides down a certain 21° slide in four times the time it would take to slide down a frictionless 21° slide. What is the coefficient of kinetic friction between the pig and the slide?

plug this into the calculator: 15/16 tan 21

To find the coefficient of kinetic friction between the pig and the slide, we can use the concept of time taken.

Let's assume that the time taken to slide down a frictionless 21° slide is represented by t.

Given that the pig slides down a certain 21° slide in four times the time it takes to slide down a frictionless slide, we can say that the time taken on the certain slide is 4t.

Now, let's consider the forces acting on the pig as it slides down the slide. We have the component of gravity acting parallel to the slide, which is mg*sin(21°), and the force of friction opposing the motion, which is μk*N, with μk being the coefficient of kinetic friction and N being the normal force.

Since the pig is sliding down at a constant velocity, we can conclude that the force of friction is equal in magnitude and opposite in direction to the parallel component of gravity.

Thus, we have μk*N = mg*sin(21°).

Next, let's consider the normal force N. It is the force exerted by the slide on the pig perpendicular to the slide. Since the pig is not sinking into the slide and is not accelerating vertically, N is equal in magnitude and opposite in direction to the perpendicular component of gravity, which is mg*cos(21°).

Substituting the value of N, we have μk*mg*cos(21°) = mg*sin(21°).

The mass of the pig cancels out, and we are left with μk*cos(21°) = sin(21°).

Dividing both sides by cos(21°), we get μk = tan(21°).

Now, we can calculate the coefficient of kinetic friction between the pig and the slide by taking the tangent of 21°.

Using a calculator, we find that tan(21°) is approximately 0.389.

Therefore, the coefficient of kinetic friction between the pig and the slide is approximately 0.389.