Block Sliding A block with mass m - 12 kg rests on a frictionless table and is a

Question

Block Sliding A block with mass m - 12 kg rests on a frictionless table and is accelerated by a spring with spring constant k 4541 N/m after being compressed a distance x1 0.443 m from the spring's unstretched length. The floor is frictionless except for a rough patch a distance d = 2.7 m long. For this rough path, the coefficient of friction is k -0.4 How much work is done by the spring as it accelerates the block? 2What is the speed of the block right after it leaves the spring? m/s Submi How much work is done by friction as the block crosses the rough spot? What is the speed of the block after it passes the rough spot? m/s Submi Instead, the spring is only compressed a distance x2-0.111 m before being released. How far into the rough path does the block slide before coming to rest? m Submit What distance does the spring need to be compressed so that the block will just barely make it past the rough patch when released?

Explanation / Answer

a) Work done W1 = 1/2 k x12

= 1/2 * 4541 * 0.4432= 445.58 J

b) 1/2 k x12 = 1/2 m v2

speed v = sqrt [ k x12 / m] = sqrt [4541 * 0.4432 / 12]

v = 8.62 m/s

c) Work done W2 = -muk m g d

= 0.4 * 12 * 9.8 * 2.7 = -127 J

d) 1/2 m v2 = W1 + W2

445.58 - 127 = 1/2 * 12 * v2

v = 7.28 m/s

e)W = 1/2 k x22 = 1/2 * 4541 * 0.1112 = 27.97 J

27.97 = muk m g d' = 0.4 * 12 * 9.8 * d'

d' = 0.595 m

f) 1/2 k x2 = muk m g d

1/2 * 4541 * x2 = 0.4 * 12 * 9.8 * 2.7

x = 0.236 m

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

---