Question

Notify Me Bookmark

The cart impacts the safety barrier with speed v0 = 4.00 m/s and is brought to a stop by the nest of nonlinear springs which provide a deceleration a = −k1x − k2x3, where x is the amount of spring deflection from the undeformed position and k1 and k2 are positive constants. If the maximum spring deflection is 490 mm and the velocity at half-maximum deflection is 3.56 m/s, determine the values for the constants k1 and k2. Answers: k1 = s−2 k2 = m−2s−2

The cart impacts the safety barrier with speed v0 = 4.00 m/s and is brought to a stop by the nest of nonlinear springs which provide a deceleration a = −k1x − k2x3, where x is the amount of spring deflection from the undeformed position and k1 and k2 are positive constants. If the maximum spring deflection is 490 mm and the velocity at half-maximum deflection is 3.56 m/s, determine the values for the constants k1 and k2. Answers: k1 = s−2 k2 = m−2s−2

Image text
The cart impacts the safety barrier with speed v 0 = 4.00 m / s and is brought to a stop by the nest of nonlinear springs which provide a deceleration a = − k 1 x − k 2 x 3 , where x is the amount of spring deflection from the undeformed position and k 1 and k 2 are positive constants. If the maximum spring deflection is 490 m m and the velocity at half-maximum deflection is 3.56 m / s , determine the values for the constants k 1 and k 2 .
Answers:
k 1 = i s − 2 k 2 = i m − 2 s − 2

Detailed Answer

0 0

Please enter your email here. You will get email when this question is answered by our tutor.

Doubtrix Logo

Problem is not yet solved!

Click on Notify me to get email when question is answered.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Notify me Login Sign Up

Similar/Related Questions

The cart impacts the safety barrier with speed v0 = 4.00 m/s and is brought to a stop by the nest of nonlinear springs which provide a deceleration a = −k1x − k2x3, where x is the amount of spring deflection from the undeformed position and k1 and k2 are positive constants. If the maximum spring deflection is 490 mm and the velocity at half-maximum deflection is 3.56 m/s, determine the values for the constants k1 and k2. Answers: k1 = s−2 k2 = m−2 s−2
Solution
0 0

A block of mass m rests on a rough horizontal surface and is attached to a spring of stiffness k. The coefficients of both static and kinetic friction are μ. The block is displaced a distance x0 to the right of the unstretched position for the spring and released from rest. If the value for x0 is large enough, the spring force will overcome the maximum available static friction force and the block will slide toward the unstretched position of the spring with an acceleration a = μg − k/mx, where x represents the amount of stretch (or compression) in the spring at any given location in the motion. Use the values m = 10 kg, k = 115 N/m, μ = 0.44, and x0 = 530 mm and determine the final spring stretch (or compression) xf when the block comes to a complete stop. The distance xf will be positive if to the right (spring stretched) and negative if to the left (spring compressed). Answer: xf = mm
Solution
0 0

A block of mass m rests on a rough horizontal surface and is attached to a spring of stiffness k. The coefficients of both static and kinetic friction are μ. The block is displaced a distance x0 to the right of the unstretched position of the spring and released from rest. If the value of X0 is large enough, the spring force will overcome the maximum available static friction force and the block will slide toward the unstretched position of the spring with an acceleration a = μg − kmx, where x represents the amount of stretch (or compression) in the spring at any given location in the motion. Use the values m = 5 kg, k = 150 N/m, μ = 0.40, and x0 = 200 mm and determine the final spring stretch (or compression) xf when the block comes to a complete stop.
Solution
0 0