Problem 4 (conservation of total mechanical energy) A train ear with a mass of m

Question

Problem 4 (conservation of total mechanical energy) A train ear with a mass of m 500kg is rolling on a frietionless track with an initial speed of 3m/, It rolls up a hill with a height of h 0.4m. After rolling up the hill the train car runs into a spring with a spring constant of k 200 lem and is brought k va a) Using the coordinate system shown determine the total mechanical energy of the system. b) Determine the speed of the train car at the top of the hill (point A). c) Determine how far the spring gets compressed in stopping the train car.

Explanation / Answer

a) total mechanical energy = PE + KE

and PE = mg h and KE = m v^2 /2

taking x axis reference point then for initial position, h = 0 and v = 3 m/s

total ME = (0 ) + (500 x 3^2 /2 ) = 2250 J

b) total energy will be conserved.

using energy conservation for point 0 and A.

PE + KE = constant

2250 = m g h + m v^2 /2

2250 = (500 x 9.8 x 0.4) + (500 v^2 /2 )

v = 1.08 m/s

C) now KE of car will convert into elatic PE of spring/

hennce elastic PE = KE

k x^2 /2 = m v^2 /2

200 x^2 / 2 = (500)(1.08^2)/2

x = 1.7 m

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

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