Susan’s 10 kg baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled 30° above the floor. The tension is a constant 30 N and the coefficient of friction is 0.20. Use work and energy to find Paul’s speed after being pulled 3.0 m.

2.37 m/s

Explanation:

From the question

W = W'-Wf Equation 1

Where W = net work done by Susan, W' = Work done by Susan, Wf = Work done against friction

W = FdcosФ-[d(mgμ-FsinФ)] Equation 2

Where F = the force applied by Susan, d  = distance, Φ = angle of the force to the horizontal, m = mass, μ = coefficient of friction, g = acceleration due to gravity.

Given: F = 30 N, d = 3 m, m = 10 kg, μ = 0.2, g = 9.8 m/s², Ф = 30°

Substitute into equation 2

W = 30(3)(cos30°)-0.6[(9.8)(10)-30sin30°]

W = 77.94-49.8

W = 28.14 J.

But,

W = 1/2mv² Equation 3

Where v = Paul's speed

make v the subject of the equation

v = √(2W/m) Equation 3

Given: W =28.14 J, m = 10 kg.

Substitute into equation 3

v = √(2×28.14/10)

v = √(56.28/10)

v =√5.628

v = 2.37 m/s

the force on the thing and the distance the force moves the thing

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