Question

A block with mass m - 17 kg rests on a frictionless table and is accelerated by a spring with spring constant k = 4267 N/m after being compressed a distance x -0.564 m from the spring's unstretched length. The floor is frictionless except for a rough patch a distanced 2.3 m long. For this rough path, the coefficient of friction is - 0.46. "How much work is done by the spring as it accelerates the block? You currently have submissions for this question, Only 10 submission are allowed You can make 10 more submissions for this question What is the speed of the block right after it leaves the spring? You currently have submissions for this question. Only 10 submission are allowed You can make 10 more submissions for this question. How much work is done by friction as the block crosses the rough spot? You currently have submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question What is the speed of the block after it passes the rough spot? m/s You currently have submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question, "Instead, the spring is only compressed a distance x2 -0.161 m before being released, How far into the rough path does the block slide before coming to rest? mw You currently have submissions for this question. Only 10 submission are allowed You can make 10 more submissions for this question. "What distance does the spring need to be compressed so that the block will just barely make it past the rough patch when released? mut You currently have submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. If the spring was compressed three times farther and then the block is released, the work done on the block by the spring as it accelerates the block is: the same three times greater three times less Onine times greater Onine times less You currently have submissions for this question. Only 10 submission are allowed You can make 10 more submissions for this question

Answer 1

The work done spring during the acceleration is, = (0.5)(4267)(0.564) = 678.66 J The speed of the block after leaving the spring is, ka? = mv2 (4267)(0.564) (17) = 8.94 m/s The work done by friction is, W = -umgd =-(0.46)(17)(9.8) (23) =-176.26 The speed of the block after passing through the rough spot is, W: +W = mv (678.66–176.26) = C1 (17)v? 12 - 678.66–176.26 8.5 = 7.69 m/s (5) The work done by the spring during the acceleration is,

W = 1 kg = {)(4267)(0.161) = 55.30 W = umgd 55.30 = (0.46 (17) (9.8)d 55.30 (0.46)(17)(9.8) = 0.72 m (6) The distance of compression is, ha? = uçmgd (0.5)(4267)x* = (0.46)(17)(9.8)(2.3) 2_(0.46)(17) (9.8)(2.3) (0.5)(4267) x=0.29 m The work done spring during the acceleration is, W3 = k(3x) = (0.5) (4267)(9)(0.564) =9WJ Nine times greater