Question

a bolck of mass 40 kg is placed at the top of a slope of a rough surface. The slope is 10 m high and its length is 100m. When the block is pushed with the initial speed of 5.0 m/s downward along the slope, find the block's speed in m/s, at the bottom of the slope. Constant friction is 20N

Answer 1

apply work energy theorem

Work done by the net force = change in mechanical energy

Net force = m*g*sin(theta) - f

f is the firctional force

theta is the angle of inclination
theta = asin(10/100) = asin(0.1) = 5.73 degrees

total energy at the top = m*g*h + 0.5*m*u^2 = (40*9.81*10) +(0.5*40*5*5) = 4424 J

total energy at the bottom = 0.5*m*v^2 = 0.5*40*v^2

then [m*g*sin(5.73) - 20]*100 = 20*v^2-4424

[40*9.81*sin(5.73) - 20 ]*100 + 4424 = 20*v^2

v = 17.8 m/s this is the required speed st the bottom of the bottom of the slope