Respuesta :
Answer:
W = (F1 - mg sin θ) L, W = -μ mg cos θ L
Explanation:
Let's use Newton's second law to find the friction force. In these problems the x axis is taken parallel to the plane and the y axis perpendicular to the plane
Y Axis
N - [tex]W_{y}[/tex] =
N = W_{y}
X axis
F1 - fr - Wₓ = 0
fr = F1 - Wₓ
Let's use trigonometry to find the components of the weight
sin θ = Wₓ / W
cos θ = W_{y} / W
Wₓ = W sin θ
W_{y} = W cos θ
We substitute
fr = F1 - W sin θ
Work is defined by
W = F .dx
W = F dx cos θ
The friction force is parallel to the plane in the negative direction and the displacement is positive along the plane, so the Angle is 180º and the cos θ= -1
W = -fr x
W = (F1 - mg sin θ) L
Another way to calculate is
fr = μ N
fr = μ W cos θ
the work is
W = -μ mg cos θ L
The normal reaction prevents the block from sinking into the inclined plane
Work done by friction on the block is μ·L·cos(θ)(F₁·sin(θ) - m·g)
The reason above expression for work done is correct is presented as follows:
The given parameters are;
The magnitude of the force acting on the block = F₁
Coefficient of kinetic friction between the plane and the block = μ
Work done by the force of friction = [tex]W_{fric}[/tex]
The angle of inclination of the plane = θ
Distance up the incline the block moves = L
Required:
The work done on the block by the force of friction, [tex]W_{fric}[/tex]
Solution:
Normal reaction, N = (m·g - F₁·sin(θ))·cos(θ)
Fictional force, [tex]F_f[/tex] = -μ·(m·g - F₁·sin(θ))·cos(θ) (opposite in direction to the applied force)
Work done = Force × Direction of the force
Work done on the block by friction, as the block moves up the inclined plane a distance, L is [tex]W_{fric}[/tex] = [tex]F_f[/tex] × L
∴ [tex]W_{fric}[/tex] = -μ·(m·g - F₁·sin(θ))·cos(θ) × L
Work done on the block by friction, as the block moves up the inclined plane a distance, L, [tex]W_{fric}[/tex] = -μ·(m·g - F₁·sin(θ))·cos(θ) × L= μ·L·F₁·cos(θ)·sin(θ) - μ·m·g·L·cos(θ) = μ·L·cos(θ)(F₁·sin(θ) - m·g)
Work done on the block by friction = μ·L·cos(θ)(F₁·sin(θ) - m·g)
Learn more about motion on an inclined plane here:
https://brainly.com/question/14020955
