Answer:
[tex]v_{f1} =\sqrt{2*(\frac{m_{2}*g }{mi+m2})*H }[/tex]
Explanation:
Newton's second law:
∑F = m*a Formula (1)
∑F : algebraic sum of the forces in Newton (N)
m : mass s (kg)
a : acceleration (m/s²)
We define the x-axis in the direction parallel to the movement of the cart and the y-axis in the direction the movement of the cylinder
Forces acting on the cart
W₁: Weight of the cart : In vertical direction (-y)
N₁ : Normal force :In vertical direction (+y)
T: tension force: In horizontal direction (+x)
Newton's second law to the cart:
∑Fx = m₁*a
T = m₁*a Equation(1)
Forces acting on the cylinder
W₂= m₂*g : Weight of m₂ : In vertical direction
T : Tension force: In vertical direction
Newton's second law to the cylinder :
We take as positive the forces that go in the same direction of the movement of the cylinder, that is, downaward:
∑Fy = m₂*a
W₂-T = m₂*a
W₂- m₂*a = T Equation(2)
Equation(1)= Equation(2) =T
m₁*a=W₂- m₂*a
m₁*a+m₂*a = W₂
a( m₁+m₂) = m₂*g
[tex]a= \frac{m_{2}*g }{m_{1}+m_{2} }[/tex]
Speed of the cart after the cylinder has descended a distance H
We apply the kinematic equation to the cart:
vf²=v₀²+2*a*d formula (2)
Where:
d:displacement in meters (m)
v₀: initial speed in m/s
vf: final speed in m/s
a: acceleration in m/s²
Data
[tex]a= \frac{m_{2}*g }{m_{1}+m_{2} }[/tex]
v₀=0
d = H
We replace data in the formula (2)
vf₁²=v₀₁²+2*a*H
[tex]v_{f1} =\sqrt{2*(\frac{m_{2}*g }{mi+m2})*H }[/tex]
