4. (15 points) Using work&energy;: A 3.50 kg block slides with vi15.12 cm/s on a

Question

4. (15 points) Using work&energy;: A 3.50 kg block slides with vi15.12 cm/s on a frictionless, straight-line track. A small electric fan is used to gently blow against the block while it slides, first in the direction the block is already sliding and then against the block's 0.6- 0.2- motion. The graph at right shows the force the fan exerts on the block as a function of the£02 block's position. a. What is the speed of the block when the 2 0.6 block is at 40.0 cm? (Answer: v = 0.237 m/s) 10 20 30 4 50 6o Distance in centimeters b. What is the fastest speed of this block? (Answer: v 0.256 m/s) When is the block moving fastest?

Explanation / Answer

given

m = 3.5 kg
vi = 15.12 cm/s = 0.1512 m/s

a) Workdone from 0 cm to 40 cm = area under F-x curve

= (1/2)*0.3*0.5 + (1/2)*0.1*(-0.3)

= 0.06 J

Now using Work-energy theorem,

Workonde = change in kinetic energy

W = (1/2)*m*(vf^2 - vi^2)

2*W/m = vf^2 - vi^2

==> vf = sqrt(2*W/m + vi^2)

= sqrt(2*0.06/3.5 + 0.1512^2)

= 0.239 m/s

b) at x = 30 cm , the block has maximum speed.

Workdone from 0 cm to 30 cm = area under F-x curve

= (1/2)*0.3*0.5

= 0.075 J

Now using Work-energy theorem,

Workonde = change in kinetic energy

W = (1/2)*m*(vf^2 - vi^2)

2*W/m = vf^2 - vi^2

==> vf = sqrt(2*W/m + vi^2)

= sqrt(2*0.075/3.5 + 0.1512^2)

= 0.256 m/s

c) The block will never have zero speed.

because, Workdone is posivtive.

net workdone = 0

d) at x = 60 cm,

vf = vi

= 0.1512 m/s

because, As net workdone is zero there is no change in kinetic energy of the block.

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.