In the figure here, a small block is sent through point A with a speed of 6.8 m/

Question

In the figure here, a small block is sent through point A with a speed of 6.8 m/s. Its path is without friction until it reaches the section of length L 14 m, where the coefficient of kinetic friction is 0.78. The indicated heights are h1 5.4 m and h2 2.8 m. What are the speeds of the block at (a) point B and (b) point C? (c) Does the block reach point D? (d) If so, what is its speed there; if not, how far through the section of friction does it travel? (a) Number Unit (b) Number Unit (d) Number Unit

Explanation / Answer

a)

(K + U)A = KB

1/2*m*VB^2 = 1/2*m*VA^2 +m*g*h1

VB = sqrt(VA^2 +2*g*h1) = sqrt(6.8^2 + 2*9.8*5.4) = 12.33 m/s

b)

KB = (K + U)C

KC = KB - UC = 1/2*m*VC^2 = 1/2*m*VB^2 - m*g*h2

VC = sqrt(VB^2 -2*g*h2) = sqrt(12.33^2 - 2*9.8*2.8) = 9.865 m/s

c)

If the work done by friction is > KC

then the block does not reach D

W = µ*m*g*L = 0.78*g*L = 0.78*9.8*14 = 107.016 J/kg

KC = 1/2*VC^2 = 1/2*9.865^2 = 48.6591 J/kg

so the block does not reach D

d)

distance travel = VC^2/2g = 9.865^2/2*9.8 = 4.965 m

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

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