Esteban pulls a 62 kg sled trough the snow. On the back of the sled is his 50 kg sack of fishing equipment. The  between the sled and the snow is 0.07 and the  between the sled and the sack is 0.1. While pulling, the fishing rod sticking out of his sack catches a tree branch, but Esteban doesn't notice and keeps walking. What force does Esteban need to exert to keep the sled moving with a constant velocity while the sack is pulled back across it?

F = 144 N

Explanation:

For this exercise we will use Neqwton's second law. Let's fix a reference system with the x-axis in the direction of the sled, let's write the forces for each part

Sack, let's use subscript 1

Y axis  

       N₁-W₁ = 0

       N₁ + W₁ = m₁ g

X axis

       fr₁ = m a₁

the expression for the friction force is

       fr = μ₁ N₁

we substitute

        μ₁ m₁ g = m a₁

Sled, subscript 2

Y axis

       N₂ - W₁ -W₂ = 0

       N₂ = W₁ + W₂

       N₂ = (m₁ + m₂) g

X axis

       F - fr₁ -fr₂ = m a₂

the expression for the deroce force is

      fr = μ N

we substitute

       F - μ₁ m₁g - μ₂ (m₁ + m₂) g = m a₂

as it indicates that the velocity is constant the acceleration of the sled is zero (a₂ = 0)

       F = μ₁  m₁g + μ₂  (m₁ + m₂) g

       F = g (m₁ (μ₁ + μ₂) + μ₂ m₂)

let's calculate

       F = 9.8 (50 (0.07 + 0.1) + 62 0.1)

       F = 144 N

ill do it for 100, also this isnt 80 its 40

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