Question

A 2.3 kg particle is projected with an initial speed of 5 m/s along a surface for which the coefficient of kinetic friction is 0.8. Find the distance it travels given that:
the particle moves down a 21 degrees incline. @Physics

Answer 1

Ok for this, uses forces to find the acceleration, then use kinematics... Im working on it now

Answer 2

2.91 m

Answer 3

okay, so first thing I did was to draw a picture, label the forces on the picture and separate the ones that werent parallel or perpendicular to the motion into components. This resulted in 4 different components of forces: The perpendicular force of gravity (Fgn), the normal force (Fn) , the force of friction (Ff) and the parallel force of gravity (Fgt). Some math followed to figure out what these all were.
\[F_{gn} = mgcos\theta = - 21.04 \]\[F_{gt} = mg sin\theta=-8.078\]\[F_n = mgcos\theta = 21.04 \]\[F_f = F_n *\mu_0 = 16.832\]

The sum of the y direction forces (Fgt & Fn) are clearly zero, while the sum of the x direction forces result in 8.754 Newtons back up the ramp. This number can be used to find the acceleration of the particle using Newton's second law.
\[\Sigma F = ma\]This ends up being 3.806 m/s/s. From here it becomes a simple kinematic problem where you know the initial velocity (5m/s down the ramp) final velocity (0) and the acceleration (3.806 m/s/s up the ramp)