A device for tensioning recording tape in a video cassete recorder is shown. the

Question

A device for tensioning recording tape in a video cassete recorder is shown. the tape wraps around small pins at A, B and C. the pins at A and C are fixed, and the pin at C is supported by the spring and can undergo vertical motion in the frictionless slot. friction between the tape and pins are negligible. The spring has a stiffness k=0.5 N/mm and is unstretched when h=25mm . Neglecting the size of the pins, determinethe tension in the tape when

a)h=18 mm

b)h=10 mm

pls answer in detail will rate lifesaver if correct :)!!!

Explanation / Answer

suppose angle BAC = , the tension is T and d = 24mm, k = 0.5N/mm

then

Tsin + Tsin - kh = 0

2Tsin = kh

T = kh / 2sin = kh /(2h/sqrt(h2 + d2)) = khsqrt(h2 + d2) / 2h

a) h = 18mm

T = 0.5(25-18) sqrt(182 + 242)/2*18 = 2.92 N

b) h = 10 mm

T = 0.5(25-10)sqrt(102 + 242)/2*10 = 9.75 N

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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