A block of mass M travels over a frictionless horizontal surface at 3.00 m/s. Th

Question

A block of mass M travels over a frictionless horizontal surface at 3.00 m/s. The block encounters a frictionless incline as shown in the figure below.

a) What vertical distance up the incline does the block travel before coming momentarily to rest.

b) Suppose a solid sphere of identical mass is rolling without slipping on a rouh surface and encounters a rough incline. If the velocity of the center of mass of rthe sphere is the sam as that of the block how far up the incline does it roll?

c) Determine the acceleration of the block and sphere if the angle is 20° and kinetics' friction coefficient is .25

5) A block of mass M travels over a frictionless horizontal surface at 3.00 m/s. The block encounters frictionless incline as shown in Figure below. a) What vertical distance up the incline does the block travel before coming b) momentarily to rest? rolling without slipping a rough of Suppose a solid sphere of identical mass is of mass surface and encounters a rough incline. If the velocity of the center it roll? the sphere is the same as that of the block how far up the incline does is 20° c) the acceleration of the block and sphere objects if the angle and kinetics' friction coefficient .25. vCM

Explanation / Answer

a) conservation of momentum

0.5 m v^2 = mgh

h = v^2 / 2g

h = 3^2 / 2*9.8

h = 0.46 m

b) 0.5mv^ + 0.5Iw^2 = mgh

0.5mv^ + 0.5(2/5 mR^2) (v/R)^2 = mgh

1/2 mv^2 + 1/5 mv^2= mgh

7/10 mv^2 = mgh

h = 7/10 * (v^2/g)

h = 0.7* (3^2 / 9.8)

h = 0.643 m

c) ma = - (mgsin 20 - u*mgcos20)

a = - (gsin 20 - u*gcos20)

a = - (9.8*sin 20 - 0.25*9.8*cos20)

a = -1.05 m/s^2

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