Question

A mass slides from rest down a 45 degree incline that has a coefficient of kinetic friction
equal to 0.2. What is the speed of the mass after it has slid for a total of 2 meters?

Answer 1

Answer:

The speed of the mass after it has slid for a total of 2 meters is 4.71 m/s.

Explanation:

The speed of the mass can be found using Newton second law:

$\Sigma F = ma$

$P_{x} - F_{\mu_{k}} = ma$

Where Pₓ is the weight force in the horizontal direction and $F_{\mu_{k}}$ is the friction force.  

$mgsin(\theta) - \mu_{k}mgcos(\theta) = ma$    

$a = g(sin(\theta) - \mu_{k}cos(\theta)) = 9.81 m/s^{2}(sin(45) - 0.2*cos(45)) = 5.55 m/s^{2}$

Now, we can find the speed of the mass using the following kinematic equation:

$v_{f}^{2} = v_{0}^{2} + 2ax$

$v_{f} = \sqrt{0 + 2*5.55 m/s^{2}*2 m} = 4.71 m/s$

Therefore, the speed of the mass after it has slid for a total of 2 meters is 4.71 m/s.

I hope it helps you!