At NASA\'s Zero Gravity Research Facility in Cleveland, Ohio, experimental paylo

Question

At NASA's Zero Gravity Research Facility in Cleveland, Ohio, experimental payloads fall freely from rest in an evacuated vertical shaft through a distance of 132 m.

(a) If a particular payload has a mass of 24 kg, what is its potential energy relative to the bottom of the shaft?

(b) How fast will the payload be traveling when it reaches the bottom of the shaft?

(c) Convert your answer to mph for a comparison to highway speeds.

A bicycle and rider going 15 m/s approach a hill. Their total mass is 86 kg.

(a) What is their kinetic energy?

(b) If the rider coasts up the hill without pedaling, how high above its starting level will the bicycle be when it finally rolls to a stop?

Explanation / Answer

a) Mass: m = 24 kg

Height (distance): d = 132 m

g = 9.8 m/s2

Potential energy: PE = mgd = 24*9.8*132 = 31046.4 J

b) Height (distance): d = 132 m

g = 9.8 m/s^2

KE = 1/2*mv^2 and PE = mgd

Conservation of energy dictates that the KE = PE. Thus we have PE = KE

0.5mv^2 = mgd

v = sqrt(2gd) = sqrt(2*9.8*132) = 50.864 = 50.9 m/s

c) Since v = 50.864 m/s = 50.864 x (1 m/s) = 50.864 x (2.24 mph) = 113.935mph = 113.9 mph rounded off

2) a) Speed: v = 15 m/s

Mass: m = 86 kg

KE = 0.5mv^2 = 0.5*86*15^2 = 9675 J

b) The kinetic energy is being transferred completely into potential.
KE = PE
9675 = mgh = 86*9.8*h
h = 11.5 meters

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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