Answer to Question #200310 in Mechanics | Relativity for Gil Dror

Question

A body is thrown at a velocity v0 up a non-smooth slope whose angle of inclination is alpha = 37 degrees. The kinetic coefficient of friction between the graph and the surface is u. The graph in front of you describes the acceleration of the body from the beginning of its movement up the slope until the moment it returns to the bottom of the slope

 A. Using the graph, determine the initial velocity V0 and calculate how many meters the body rose along the slope in. B. Using the graph, determine the final velocity of the body when it reaches the bottom of the slope.

 C. Draw a graph of the velocity of the body from the moment it is thrown up the sloping plane until it returns to the bottom of the plane. 

D. Indicate in your notebook the diagrams of the forces acting on the body during the ascent and during the descent. 

E. Calculate u 

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Answer 1

A.

Acceleration from start to the highest point (t=3 sec):

$a_1=\frac{0-v_0}{3}=-\frac{v_0}{3}=-7.6\ m/s^2$

$v_0=3\cdot7.6=22.8\ m/s$

Length of rising:

$L=v_0t+at^2/2=22.8\cdot3-7.6\cdot3^2/2=34.2\ m$

B.

Acceleration from the highest point to the bottom:

$a_2=\frac{v}{6.94-3}=4.4\ m/s^2$

Final velocity:

$v_1=3.94\cdot4.4=17.3\ m/s$

C.

Velocity of moving up:

$v=v_0+a_1t$ , $0\le t\le3$

$v=22.8-7.6t$

Velocity of moving down:

$v=a_2(t-3)$ , $3\le t\le6.94$

$v=4.4(t-3)$

D.

E.

Equations of moving down:

$ma_2=mgsin\alpha-Nu$

$0=mgcos\alpha-N$

The kinetic coefficient of friction:

$u=\frac{gsin\alpha-a_2}{gcos\alpha}=\frac{9.8sin37\degree-4.4}{9.8cos37\degree}=0.191$