Question

ECTION C: FUNDAMENTAL PROBLEMS Note: Show every details of work to get full credit in workout problems.) 6. A 8.0-kg block slides down a smooth inclined plane. The plane is 20.0 m long and is inclined at an angle of 40° with the horizontal. Find (a) the acceleration of the block, and (b) the velocity of the block at the bottom of the plane. 40° .) Draw free-body diagram in the above figure. (Show your X- and y-axes and all the forces acting on the block).

Answer 1

here,

mass of block , m = 8 kg

s = 20 m

theta = 40 degree

a)

b)

for y- axis

Normal force , N= m * g * cos(theta)

for x-axis

using Newton's second law

m * a = m * g * sin(theta)

a = g * sin(theta)

c)

a = g * sin(theta)

a = 9.81 * sin(40) = 6.31 m/s^2

the acceleration of the block is 6.31 m/s^2

d)

the velocity of block at the bottom of the incline , v= sqrt(2 * a * s)

v = sqrt(2 * 6.31 * 20) m/s

v = 15.88 m/s