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rjkz [21]
3 years ago
11

Jay fills a wagon with sand (about 20 kg) and pulls it with a rope 40 m along the beach. He holds the rope 25â above the horizon

tal. The rope exerts a 20-N tension force on the wagon. How much work does the rope do on the wagon?
Physics
1 answer:
never [62]3 years ago
8 0

Answer:

W = 725 J

Explanation:

given,

mass of wagon = 20 kg

distance of pull = 40 m

angle made with the horizontal = 25°

tension force on the wagon = 20 N

Work done = ?

Horizontal component of the force will help in movement of the wagon.

Horizontal component of force=

F_x = F cos θ

Work done is equal to force into displacement

W = F.s

W =  F cos θ.s

W = 20 cos 25° x 40

W = 725 J

hence, work done on pulling the wagon is equal to W = 725 J

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Nomenclature

vf: final velocity

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a: acceleleration

d: distance

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W: weight

m:mass

g: acceleration due to gravity

Graphic attached

The attached graph describes the variables related to the kinetics of the object (forces and accelerations)

Calculation de of the components of W in the inclined plane

W=m*g

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-μ₁N₁+Wx₁ = ma₁      Equation (2)

∑Fy₁=0   : Newton's first law

N₁-Wy₁= 0

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N₁  =  m*g*cos30°

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-μ₁*g*cos30°+g*sin30° = a₁  

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a₁ =9.8(-0.2*cos30°+sin30°)=3.2 m/s²

We replace a₁ =3.2 m/s² and d₁= 3m in the equation (1)

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Rough surface  kinetics (μ= 0.3)

∑Fx₂=ma₂  :Newton's second law

-Ff₂=ma₂

--μ₂*N₂ = ma₂   Equation (4)

∑Fy₂= 0  :Newton's first law

N₂-W=0

N₂=W=m*g

We replace N₂=m*g inthe equation (4)

--μ₂*m*g = ma₂   We divide by m

--μ₂*g = a₂

a₂ =-0.2*9.8= -1.96m/s²

We replace a₂ = -1.96m/s² in the equation (3)

0   =4.38²+2*-1.96*d₂

3.92*d₂ = 4.38²

d₂=4.38²/3.92

d₂=4.38²/3.92

(a-1) d₂=4.89 m: The object slides 4.89 m along the rough surface

(a-2) Work (Wf) done by the friction force while the mass is sliding down the in- clined plane:

Wf = - Ff₁*d₁

Ff₁= μ₁N₁= μ₁*m*g*cos30°= -0.2*4*9.8*cos30° = 6,79 N

Wf= -  6.79*3 = 20.4 N*m

Wf=  -20.4 J    is negative

(b) Work (Wg) done by the gravitational force while the mass is sliding down the inclined plane

Wg=W₁x*d= m*g*sin30*3=4*9.8*0.5*3= 58.8 N*m

Wg= 58.8 J is positive

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