Problem 7.67 Blocks with different masses are pushed against a spring one at a t

Question

Problem 7.67 Blocks with different masses are pushed against a spring one at a time, compressing it different amounts. Each is then launched onto an essentially frictionless horizontal surface that then curves upward, still frictionless (Figure 1). The table below shows the masses, spring compressions, and maximum vertical height each block achieves. Mass m (g) Compression E (cm) 2.40 3.17 5.40 4.29 1.83 Height h (cm) 50.0 85.2 128 50.0 85.2 10.3 11.2 19.8 35.2 3.81 Part C of 1 Determine the spring constant k using a best-fit line. Express your answer to two significant figures and include the appropriate units. kValue Submit My Answers Give Up Frictionless Incorrect; Try Again; no points deducted

Explanation / Answer

Force constant k=f/x

from law of conservasion of energy .potential energy of spring is given as-----

mgh=1/2 kx2

k1=2m1gh1/x12=( 2x50x980x10.3)/2.402=1009400/5.76=175243.05/1000=175.243N/m------------------(accleration due to gravity=980cm/s2)-----------------dyne/cm= 1/1000 (N/m)

k2=2m2gh2/x22= (2x85.2x980x11.2)/3.172 = 1870310/10.04=186285/1000=186.285N/m

k3=2m3gh3/x32=(2x126x980x19.8)/5.402= 4889808/29.16=167688/1000=167.688N/m

k4=2m4gh4/x42=(2x50x980x35.2)/4.292=34496/18.40=187478/1000=187.478N/m

k5=2m5gh5/x52=(2x85.2x980x3.81)/1.832=626339/3.34=190440/1000=190.440N/m

force constant k=(k1+k2+k3+k4+k5)/5=(175.243+186.285+167.688+187.478+190.440)/5=907.134/5=181.4268N/m

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---