In the above figure, a block is sliding along asurface with a = 0.2 coefficient

Question

In the above figure, a block is sliding along asurface with a = 0.2 coefficient of dynamic friction. As the block slides, itbreaks through a paper wall that provides an impact force on theblock. Initially, the block is 10 [m] from the paper wall. Theblock comes to a stop 8 [m] beyond the paper wall.
a) What is the velocity of the block just before impact withthe wall?

b) What is the velocity of the block just after impact withthe wall?
c) How much energy is lost as the block breaks through thewall?

d) If the impact with the paper wall took 0.15 [s],what force did the wall exert on the block?

e) What is the total work done byfriction?

Explanation / Answer

a) need acceleration to get from starting velocity to velocitybefore impact
Ff = FN = mg= ma => a = g =.2(9.81m/s2) = 1.962 m/s2 to theleft
using the kinematic formua Vf2 =Vo2 + 2ax
V2 = 102 + 2(-1.962)(10) =60.76 => V=7.795 m/s    (answer to part A)
b) work backwards from final V=0 to find Vo, thevelocity just after impact is finished acceleration is the same, because once the impact is finishedthe only force on the block is the force of friction
Vf2 =Vo2 + 2ax 0 = Vo2 + 2(-1.962)(10)   => Vo2 = 39.24 => 6.264 m/s   (answer to part B)
c) wall considered too thin to have any width no change in potential energy all change in kinetic energy = (1/2)mV2
KEbefore - KEafter =KElost
(1/2)mVbefore2 -(1/2)mVafter2 = Energylost (1/2)m(Vb2-Va2) =Energy lost
(1/2)(5)(7.7952-6.2642) = Energy lost =53.81 J (answer to part C)
d) Impulse = change in momentum = mV = force * time
F = m(V1-V2)/t
F = 5(7.795-6.264)/.15 = 51.03N        (answer to part D)
e) W = Fx W = Ff(xbeforewall + xafter wall) W = FN(xbeforewall + xafter wall) W = mg(xbeforewall + xafter wall) W = .2(5)(9.81)(10+8) = 176.58 J   (answer to part E)


I hope everything was clear and that this helps!

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

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