2. Chapter 10 Conceptual Questions: (a) A roller coaster rolls down a frictionle

Question

2. Chapter 10 Conceptual Questions: (a) A roller coaster rolls down a frictionless track, reaching a speed vo at the bottom. If you want the car to go twice as fast at the bottom, by what factor must you increase the height of the track? U xhal (b) A spring has an unstretched length of 10cm. It exerts a restoring force F when stretched to a length of 11 cm. For what length of the spring is its restoring force 3F? New length a cm (c) A spring gun shoots out a plastic ball at speed to. The spring is then compressed twice the distance it was on the first shot. By what factor is the ball's speed increased?

Explanation / Answer

a) from energy conservation:

m g h0 = 1/2 m v0^2

v0^2 = 2 g h0

(2v0)^2 = 2 g H

v0^2/4 v0^2 = 2 g h0/2 g H

H = 4 h0

Hence, h(new) = 4 h(old)

b)L = 10 cm ;

x = 11 - 10 = 1 cm

F = kx = k (1 cm)

3F = k X

F/3F = 1/X => X = 3 cm

Hence, New length = X = 3 cm

c)from energy conservation:

1/2 k x^2 = 1/2 m v^2

v = x sqrt (k/m)

v' = 2 x sqrt (k/m)

v/v' = x sqrt(k/m)/2xsqrt(k/m) = 1/2

v' = 2v

v(new) = 2 v(old)

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

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