Question

At the State Fair you see people trying to win a prize at a game booth. They are sliding a metal disk shaped like a puck up a wooden ramp so that it stops in a marked zone near the top of the ramp before sliding back down. You estimate that you can slide the disk at 8.0 ft/sec, but would that win the game? The two boundaries of the zone appear to be at 10 and 10.5 feet from the bottom of the ramp where you release the disk. The ramp appears to be inclined at 37 degrees from the horizontal. To determine if you win, you decide to find how far you can slide the disk in the game. The coefficients of static and kinetic friction between steel and wood are 0.1 and 0.08, respectively. The weight of the disk is about 2.5 lbs.

I have approached this problem three different times. I don't understand. Help!

Answer 1

ทุ CO ma Cos Co

perpendicular to incline , force equation is given as

F_n = mg Cos$\theta$

kinetic frictional force is given as

f_k = u_k F_n

f_k = u_k mg Cos$\theta$

parallel to incline , force equation is given as

f_k + mg Sin$\theta$ = ma

u_k mg Cos$\theta$ + mg Sin$\theta$ = ma

a = u_k g Cos$\theta$ + g Sin$\theta$

a = (0.08) (32.2) Cos37 + (32.2) Sin37

a = 21.4 ft/s²

consider the motion parallel to incline assuming up along the incline and positive direction

a = - 21.4 ft/s²

v_i = initial velocity = 8 ft/s

v_f = final velocity = 0 ft/s

d = distance travelled before stopping

using the equation

v_f² = v_i² + 2a d

0² = 8² + 2 (-21.4) d

d = 1.5 ft