work and energy

2006-10-23 8:32 pm
Susan's 10kg brother Paul sits on a mat.Susan pulls the mat across the floor using a rope that is angled 30 degrees above the floor.The tension is a constant 30N and the coefficient of frictionis 0.20. Use work and energy to find Paul's speed after being pulled 3.0m.

answer:2.37m/s

Steps?

回答 (1)

2006-10-23 9:02 pm
✔ 最佳答案
first step u need to do is to break all the force component into X and Y (vertical n horizontal)

Forces on the rope is 30N @ 30 degree
F(ropeX) = 30*cos30 = 25.98N right
F(ropeY) = 30*sin30 = 15N up

Now calculate force acting on Paul
F(pauly) = mg = 10kg * 9.8 = 98N

Now calculate the friction force acting on Paul
F(friction) = friction coeff * force acting down = uF(down)
F(down) = F(pauly) - F(ropeY) becoz the rope pull paul up abit
therefore:
F(friction) = 0.20 * (98N - 15N) = 16.6 N Left

Now calculate the total force in Y direction:
F(totalY) = F(ropeY) - F(friction) = 25.98 - 16.6 = 9.38N

Now calculate energy or work done
W = force * distance = F(totalY) * distance = 9.38*3 = 28.14 J

Now calculate speed:
we know that
E = 1/2 mv^2
28.14 = 1/2 * 10 * v^2

so V = 2.37 m/2
參考: me


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