Problem 2 A cart gliding on a track with negligible friction collides with a spr

Question

Problem 2 A cart gliding on a track with negligible friction collides with a spring that is fixed at the end of the track. The cart is initially traveling at-2.5 and has an inertia of kg. The spring is perfectly elastic, with he cart compresses the spring, and bounces back at the same speed it had coming in (a)How far does the spring compress? (b)What is the maximum force on the cart by the spring? (c)Over the entire collision between the cart and the spring (the complete compression and re-extension of spring), what is the impulse delivered to the cart by the spring? (d)On the axes above, sketch what the graph might look like for the force on the cart by the spring during the interaction. What does the area under this graph represent? (e)How much work is done on the cart during compression of the spring (system is cart only)? (f)Assuming that the total time for the interaction between the spring and cart was 0.10s, what was the average power delivered by the spring to the cart during compression? Remember, the interaction includes the compression and the extension of the spring. (g)How much work is done on the cart (system is cart only) for the entire interval to return it to its initial speed? Prove or explain

Explanation / Answer

1. Since cart is travelling at speed of 2.5 m/s and when it is in a position where it is about to rebound then velocity is zero and the entire process takes 0.1 sec. so acceleartion is

Acc = (Vi-Vf)/t

                =2.5/0.1

                a=0.25 m/s2

now, Force = mass x acc

                        = 0.5 x 0.25

                         = 0.125 N

Now suppose contraction in spring is “y”

Then Force exerted by spring = ky

                                                          = 300 * y

Hence, y=(0.125)/300

                = 0.42 mm

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

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