Question

A ship is launched toward the water on a slipway making an angle of 5 degree with horizontal. The coefficient of kinetic friction between the bottom of the ship and slipway is 0.08. What is the acceleration of the ship along the slipway.?

Answer 1

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

Learn more about Newton's second law here:

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