May i get help with 6.5 I apply a horizontal force of 412.0 N to a 6.30 kg mass
ID: 1998726 • Letter: M
Question
May i get help with 6.5 I apply a horizontal force of 412.0 N to a 6.30 kg mass attached to a horizontally placed spring. The mass is on a horizontal frictionless surface. If the force compresses the spring by 27.0 cm, what is the spring constant for the spring? When I release the mass, what is its acceleration? Use the conservation of energy to determine the velocity of the mass when it reaches the equilibrium point, where the spring extension is zero. An insect trapped in a spider's web is subject to a restoring force of a Hooke's Law type. As it struggles the web is distorted and spring type forces act to keep the web flat. So it is possible to ascribe an effective spring constant to the web. Using sense organs in their legs, spiders can detect vibrations in their webs when their prey is captured. In this particular example a one gramme insect causes the web to vibrate 15 times a second, i.e. the web completes 15 oscillations per second. (a) What is the period for one oscillation? (b) What is the spring constant of the web? (c) If a 4.0 g insect was caught in the web, what would be the number of web oscillations in one second??Explanation / Answer
6.5) Fnet = kx - F = 0
k = 412 / 0.27 =1526 N/m .....Ans
F = kx
a = F/m = kx/m = (1526 x 0.27) / 6.30 = 65.4 m/s^2 .......Ans
Applying energy conservation,
k x^2 /2 = m v^2 / 2
1526 (0.27^2) = 6.30 v^2
v = 4.20 m/s