ONE END OF A SPRING IS ATTACHED TO A SOLID WALL WHILE THE OTHEREND JUST REACHES

Question

ONE END OF A SPRING IS ATTACHED TO A SOLID WALL WHILE THE OTHEREND JUST REACHES TO THE EDGE OF A HORIZONTAL, FRICTIONLESSTABLETOP, WHICH IS A DISTANCE H ABOVE THE FLOOR. A BLOCK OFMASS M   IS PLACED AGAINST THE END OF THE SPRINGAND PUSHED TOWARD THE WALL UNTIL THE SPRING HAS BEEN COMPRESSED ADISTANCE X, .   THE BLOCK IS RELEASED, FOLLOWS THETRAJECTORY SHOWN, AND STRIKES THE FLOOR A HORIZONTAL DISTANCE DFROM THE EDGE OF THE TABLE. AIR RESISTANCE IS NEGLIGIBLE.

DETERMINE EXPRESSIONS FOR THE FOLLOWING QUANTITIES IN TERMS OFM, X, D, H, AND G. NOTE THAT THESE SYMBOLS DO NOT INCLUDE THESPRING CONSTANT.

Explanation / Answer

A)The angle made by the block with the horizontal as itstrikes the floor is tan = (H/D) or = tan-1(H/D) ----------(1) the time elapsed from the instant the block leaves the tableto the instant it strikes the floor is t = (u * sin/g) u is the initial speed of the block,the value of isobtained from equation (1) and g is the acceleration due togravity the kinetic energy of the block as it leaves the tabletop isequal to the kinetic energy of the compressed spring when it isreleased therefore (1/2)M * v^2 = (1/2)k * x^2 or v = (k/M) * x k is the spring constant of the spring,m is the mass of thespring and x is the distance by which the spring iscompressed B)the horizontal component of the velocity of the block justbefore it hits the floor is ux= u * cos C)The work done on the block by the spring is W = (1/2)k * x^2 k is the spring constant and x is the distance by which thespring is compressed D)the spring constant of the spring is constant and has aspecific value.

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

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