A spring with spring constant 29 N/m is compressed a distance of 8.0 cm by a bal

Question

A spring with spring constant 29 N/m is compressed a distance of 8.0 cm by a ball with a mass of 219.5 g (see figure below). The ball is then released and rolls without slipping along a horizontal surface, leaving the spring at point A. The process is repeated, using a block instead, with a mass identical to that of the ball. The block compresses the spring by 8.0 cm and is also released, leaving the spring at point A. Assume the ball rolls, but ignore other effects of friction. (Assume that the ball is a solid ball.)

(a) What is the speed of the ball at point B?

(b) What is the speed of the block at point B?

Explanation / Answer

a)

I = moment of inertia of ball = 2/5 mr2

using conservation of energy

spring potential energy = kinetic energy of ball + rotational kinetic energy of ball

(0.5) k x2 = (0.5) m v2 + (0.5) I w2

k x2 = m v2 + (2mr2/5) (v/r)2

k x2 = m v2 + (2/5) m v2

k x2 = (7/5) m v2

(29) (0.08)2 = (7/5) (0.2195) v2

v = 0.78 m/s

b)

using conservation of energy

spring potential energy = kinetic energy of ball + rotational kinetic energy of ball

(0.5) k x2 = (0.5) m v2

k x2 = m v2

k x2 = m v2

(29) (0.08)2 = (0.2195) v2

v = 0.92 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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