You are standing at the very rear of a raft of length L = 5.6 m and mass M = 112

Question

You are standing at the very rear of a raft of length L = 5.6 m and mass M = 112 kg that is at rest in a lake with its prow only 0.50 m from the end of the pier. Your mass is m = 63 kg. Neglect frictional forces between the raft and the water.

(a) How far from the end of the pier is the center of mass of the you-raft system?
m

(b) You walk to the front of the raft and then stop. How far from the end of the pier is the center of mass now?
m

(c) When you are at the front of the raft, how far are you from the end of the pier?
  m

Explanation / Answer

a)

m = 63 kg = our mass

M = 112 kg = mass of raft

consider the end of pier as origin

position of center of mass of raft = Xr = L/2 + 0.5 = 5.6 /2 + 0.5 = 3.3 m,

position of our center of mass = Xp = L + 0.5 = 5.6 + 0.5 = 6.1 m

using the formula

Xcm = (M Xr + m Xp ) / (M + m)

Xcm = (112 x 3.3 + 63 x 6.1) (112 + 63)

Xcm = 4.31 m

b)

let the distance from edge of pier is now "d"

position of center of mass of raft = Xr = L/2 + d = 5.6 /2 + d = 3.3 + d ,

position of our center of mass = Xp = d

using the formula

Xcm = (M Xr + m Xp ) / (M + m)

center of mass of system remains at the same location

4.31 + d = (112 (3.3 + d) + 63 d) (112 + 63)

d = - 2.11

new location of center of mass = 4.31 - 2.11 = 2.2 m

c)

d = 2.11 m

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

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