Respuesta :
The speed of the block as it hits the ground is 3.4 m/s.
Calculation:
By Newton's Second Law:
The gravity of this M kg block is Mg, which causes the acceleration of itself downward and causes the rotational acceleration of the cylinder (mass m):
Mg = Ma + ((mr^2)*a/r)/r = (M+m)a
thus a = Mg/(M+m)
Since the distance of the movement is 1m, we have;
0.5*at^2 = 1, or v^2 = (at)^2 = 2a = 2Mg/(M+m)
v = sqrt(2*3.0*9.8/5.0) = 3.4 (m/s)
By conservation of energy:
The initial potential energy: Mgh = Mg
The final kinetic energy: 0.5Mv^2 + 0.5I*w^2
= 0.5Mv^2 + 0.5(m*r^2)*(v/r)^2
= 0.5*(M+m)*v^2
Before M hits the ground, all the potential energy would be converted to kinetic energy:
Mg = 0.5*(M+m)*v^2
or v = sqrt(2*M*g/(M+m)) = 3.4 (m/s)
Newton's second law states that the acceleration of an object is directly related to its net force and inversely proportional to its mass. A body's acceleration depends on its two components: force and mass.
Learn more about Newton's second law here:- https://brainly.com/question/25545050
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