Newton's second law for translational and rotational motion we can find the answer for the acceleration of the body is 0.04 m / s²
Newton's second law says that the sum of the external forces is equal to the product of the mass and the acceleration of a body.
Reference systems are coordinate systems with respect to which to measure and decompose the vectors, in this case we will use a regency system with the x=axis parallel to the plane and a positive direction in the direction of movement, eg the y-axis is perpendicular to the plane. .
In the Attachment we have a free-body diagram of the systems
y-axis
N - = 0
N =
x-axis
Wₓ -fr - T = m a
The friction force is the macroscopic manifestation of the microscopic interactions between the two surfaces, it is represented by the relationship
fr = μ N
Let's use trigonometry to break down the weight
cos 37 =
sin 37 =
= W cos 37
Wₓ = W sin 37
Let's substitute
N = mg cos 37
mg sin 37 - μ m g cos 37 - T = m a (1)
We use Newton's second law for rotational motion, in the pulley
τ = I α
T R = I α (2)
The weight and the normal of the pulley pass through its axis of rotation, so the distance is zero and they do not create torque
Linear and rotational variables
a = α R
α = a / R
Let's substitute in equation 2
T R = I a / R
T = I / R² a
Let's substitute in equation 1
mg sin 37 - very m g cos 37 - = m a
a =
Let's calculate
a =
a =
a = 0.39 m / s²
In conclusion using Newton's second law for translational and rotational motion we can find the answer for the eceleration of the body is
0.39 m /s²
Learn more about Newton's second law here:
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