Newton's second law we can find the acceleration of the ship is
a = 0.074 m / s²
Given parameters
- The very coefficient of kinematic friction = 0.08
- The angle of the ramp tea = 5º
To find
- The acceleration of the ship
Newton's second law states that the force varies linearly with the mass and acceleration of the body
∑ F = m a
The bold indicate vectors, where F is the sum of the forces, m the masses and the acceleration
The force is a vector magnitude, therefore it must be solved for each axis of a coordinate system, in the exerted of inclined ramps the coordinate system used has the x-axis in the direction of the ramp and the y-axis perpendicular to it, see attached. In this cordinate system the weight of the body must be decomposed.
cos 5 = W_y / W
sin 5 = Wₓ / W
W_y = W cos 5
Wₓ = W sin 5
Let's solve Newton's second law for each axis
Y axis
N - W_y = 0
N = W_y = mg cos 5
X axis
Wₓ - fr = m a (1)
Friction force is the macroscopic result of contact interactions between two bodies and is described for solids by the expression
fr = μ N
fr = μ mg cos 5
we substitute in equation 1
mg sin 5 - μ m g cos 5 = m a
a = g (sin 5 - μ cos 5)
let's calculate
a = 9.8 (sin 5 - 0.08 cos 5)
a = 0.073 m / s²
In conclusion using Newton's second law we can find the acceleration of the ship is
a = 0.073 m / s²
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