You have devised an experiment to measure the kinetic coefficient of friction between a ramp and block. You place the block on the ramp at an angle high enough that it starts sliding. You measure the time it takes to fall down a known distance. The time it takes to fall down the ramp starting from a standstill is 0.5 sec, = 1 kg, θ = 45o, and the distance it falls, L, is 0.5 m. What is µk? (8 pts)

 μ = 0.423

Explanation:

To solve this exercise we must use Newton's second law and kinematics together, let's start using expressions of kinematics to find the acceleration of the body

Let's fix a reference system where the x axis is parallel to the inclined plane, but the acceleration is only on this axis

            x = v₀ t + ½ a t²

The body starts from rest so its initial speed is zero

            a = 2 x / t²

            a = 2 0.5 /0.5²

            a = 4 m / s²

Taking the acceleration of the body, we use Newton's second law, we take the direction up the plane as positive

  X axis

                fr - Wₓ = m a          (1)

  Y Axis  

               N- = 0

                N = W_{y}

We use trigonometry to find the components of the weight

            sin 45 = Wₓ / W

           cos 45 = W_{y} / W

           Wₓ = W sin 45

           W_{y} = W cos 45

The out of touch has the expression

             fr = μ N

             fr = μ W_{y}

We substitute in 1

             μ mg cos 45 - mg sin 45 = m a

             W_{y} = (a + g sin 45) / g cos 45

              μ = a / g cos 45 + 1

We calculate

Acceleration goes down the plane, so it is negative

           a = -4 m / s²

            μ = 1- 4 / (9.8 cos 45)

            μ = 0.423

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.