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Luyando wants to have a bit of fun with her wagon. She puts her 12 𝑘𝑔 baby sister, Waluse, on the wagon and pulls it across the floor using a rope at an angle of 22° above the floor. Using the spring balance that mum uses to weigh things in the kitchen, Luyando realises that the tension in the rope is constant and has a value of about 40 𝑁. Use the work-energy theorem to find Waluse’s speed after being pulled 4.0 𝑚 across the living room. The coefficient of friction is 0.2 and the weight of the wagon is 3 𝑘𝑔.

Luyando wants to have a bit of fun with her wagon. She puts her 12 𝑘𝑔 baby sister, Waluse, on the wagon and pulls it across the floor using a rope at an angle of 22° above the floor. Using the spring balance that mum uses to weigh things in the kitchen, Luyando realises that the tension in the rope is constant and has a value of about 40 𝑁. Use the work-energy theorem to find Waluse’s speed after being pulled 4.0 𝑚 across the living room. The coefficient of friction is 0.2 and the weight of the wagon is 3 𝑘𝑔.

Grade:12

1 Answers

Moses kelvin
15 Points
3 years ago
 
Total mass being pulled = (12 + 3)kg = 15kg
Distance moved = 4m
Tension in the rope = 40N
Co-efficient of friction = 0.2
Using the work-energy theorem,
Work done by luyando in pulling her baby sister and the wagon = kinetic energy gained by waluse and wagon.
Hence,
W = K.e
Resultant weight force actin on the ground = Wn = mg - Ty = R
Ty = Tsin∅ 
R = mg - Tsin∅ 
Horizontal force moving the wagon and waluse = Tx 
Tx = Tcos∅
μ = Fᵣ/R
Fᵣ = μR
Fᵣ = μ(mg - Tsin⍉)
Fᵣ= μmg - μTsin⍉
According to newton's second law,
ΣF = ma
ΣF = Tx - Fr = ma
ΣF = Tcos⍉ -(μmg - μTsin⍉)
ΣF = Tcos⍉ - μmg + μTsin⍉ 
W = ΣFcos⍉ × D
W = (Tcos⍉ - μmg + μTsin⍉)Dcos⍉
W = k.e
(Tcos⍉ - μmg + Tsin⍉ )Dcos⍉ = 1/2mv²
[(40cos22) - (0.2×15×9.89 + (0.2×40sin22)]4cos22 = 1/2×15×v²
=> 39.637 = 7.5v²
v² = 5.2849
v = √5.2849
v = 2.2989~2.3m/s

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