A light spring with force constant 3.20 N/m is compressed by 8.56 cm as it is he

Question

A light spring with force constant 3.20 N/m is compressed by 8.56 cm as it is held between a 0.249 kg block on the left and a 0.498 kg block on the right, both resting on a horizontal surface. The spring exerts a force on each block, tending to push them apart. The blocks are simultaneously released from rest. Find the acceleration with which each block starts to move, given that the coefficient of kinetic friction between each block and the surface is the following values. (Let the coordinate system be positive to the right and negative to the left. Be sure to include the sign to indicate the direction of the acceleration.) (a) Coefficient of Kinetic Friction = 0 heavier block ___m/s^2 lighter block ___m/s^2 (b) Coefficient of Kinetic Friction = 0.070 heavier block ___m/s^2 lighter block ___m/s^2 (c) Coefficient of Kinetic Friction = 0.132 heavier block ___m/s^2 lighter block ___m/s^2

Explanation / Answer

a)

when k = 0

then ,

spring force = 3.20*0.0856

= .2739 N

let the acceleration of lighter & heavier block be denoted by 'al' & 'ah' respectively

friction force on the lighterblock =0 * mg = 0

- .2739 = 0.249*al

al = -1.1 m/s^2

friction force on tyhe heavy block = 0

hence,

.2739 = 0.498*ah

ah = .55 m/s^2

b)

for when k = 0.070

spring force = 3.20*0.0856

= .2739 N

friction force on the lighterblock =0.070 * .249*9.81

= 0.171 N

since, spring force > friction force

- .2739 + 0.171= 0.249*al

al = -0.188 m/s^2

friction force on the heavy block = 0.070*.498*9.81

= .341

since, spring force< friction froce

hence,heavier block will not move

ah = 0

c) when  k = 0.132

spring force = 3.20*0.0856

= .2739 N

friction force on the lighterblock =0.132 * .249*9.81

= 0.322 N

since, spring force < friction force

hence, lighter block will not move

al=0

friction force on the heavy block = 0.132*.498*9.81

= .645 N

since, spring force< friction froce

hence,heavier block will not move

ah = 0

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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