An 80-kg person stands at one end of a 130-kg boat. He then walks to the...

An 80-kg person stands at one end of a 130-kg boat. He then walks to the other end of the boat so that the boat moves 80 cm with respect to the bottom of the lake.

A. What is the length of the boat?

B. How much did the center of mass of the person-boat system move when the person walked from one end to the other?

Expert Solution

Let length of boat = L cm

Suppose we have a coordinate system relative to the bottom of the lake with:
Boat's position initially from x=0 cm to x=L cm
Suppose person (S) initially at x= L cm (right hand end of boat)
Let Boat's centre of mass at x = C cm

The overall (system's) initial centre of mass is at X1 where (taking moments about x=0):
(80+130)X1 = 130C + 80L (i)
After S walks left to the other end of the boat, the boat moves right 80cm.

Boat's position is now from x=80 cm to x=(L+ 80) cm
S's position is x = 80 (left end of boat)
Boat's centre of mass is at C+80

The overall (system's) final centre of mass is at X2 where (taking moments about x=0):
(80+130)X2 = (130)(C+80) + 80*80 (ii)
Since no external forces acted on the system, the system's centre of mass has not moved, so X1=X2. This means the left hand sides of both equations (i)and (ii) are equal. So we can equate the right hand sides giving:
130C + 80L = (130)(C+80) + 80*80
. 80L=16800 cm

L=210 cm=2.1 m

Length of boat=2.1 m

(B)center of mass of the person-boat system did not move when the person walked from one end to the other because there was no external force.

genius_generous answered 1 year ago

3)A person with mass m1 = 80 kg stands at the left end of a uniform...

3)A person with mass m1 = 80 kg stands at the left end of a uniform beam with mass m2 = 100 kg and a length L = 4.0 m. Another person with mass m3 = 110 kg stands on the far right end of the beam and holds a medicine ball with mass m4 = 10 kg (assume that the medicine ball is at the far right end of the beam as well). Let the origin of our coordinate...

A person with mass m1 = 68 kg stands at the left end of a uniform...

A person with mass m1 = 68 kg stands at the left end of a uniform beam with mass m2 = 109 kg and a length L = 2.5 m. Another person with mass m3 = 50 kg stands on the far right end of the beam and holds a medicine ball with mass m4 = 8 kg (assume that the medicine ball is at the far right end of the beam as well). Let the origin of our coordinate...

A) An 80- kg man stands in an elevator. What force does he exert on the...

A) An 80- kg man stands in an elevator. What force does he exert on the floor of the elevator under the following conditions? The elevator is stationary. B) The elevator accelerates upward at 2.2 m/s2. C) The elevator rises with constant velocity of 4.5 m/s. D) While going up, the elevator accelerates downward at 1.8 m/s2. The elevator goes down with constant velocity of 7.2 m/s.

Bonham the dog stands at the far end of a 14 ft, uniform boat pointing to...

Bonham the dog stands at the far end of a 14 ft, uniform boat pointing to shore (the drawings below are not exactly to scale). The boat is twice as massive as Bonham. Initially, the dog is 20 ft from shore. Eying his owner on shore, Bonham trots to the front of the boat and stops. Assuming no friction and no water current, and also that he walks the full 14 ft length of the boat (meaning his length is...

A 67.1 kg person on a diet stands on a bathroom scale in an elevator. To...

A 67.1 kg person on a diet stands on a bathroom scale in an elevator. To their great pleasure the scale reads 51.7 kg. What is the acceleration (in m/s^2) of the elevator?

A person with mass mp = 70 kg stands on a spinning platform disk with a...

A person with mass mp = 70 kg stands on a spinning platform disk with a radius of R = 2.1 m and mass md= 187 kg. The disk is initially spinning at ω = 1.4 rad/s. The person then walks 2/3 of the way toward the center of the disk (ending 0.7 m from the center). 1. What is the total moment of inertia of the system about the center of the disk when the person stands on the...

A person with mass mp = 78 kg stands on a spinning platform disk with a...

A person with mass mp = 78 kg stands on a spinning platform disk with a radius of R = 2.37 m and mass md = 198 kg. The disk is initially spinning at ω = 1.4 rad/s. The person then walks 2/3 of the way toward the center of the disk (ending 0.79 m from the center). 1)What is the total moment of inertia of the system about the center of the disk when the person stands on the...

An 80-kg person whose surface area is 1.30 m2 worked for one hour at a distance...

An 80-kg person whose surface area is 1.30 m2 worked for one hour at a distance of 2.0 meters from a spherically-symmetric source of radiation whose output power is 0.35 W. What dose (in rads) did he receive?

- An 80 kg man stands in a very strong wind moving at 13 m/s at...

- An 80 kg man stands in a very strong wind moving at 13 m/s at torso height. As you know, he will need to lean in to the wind, and we can model the situation to see why. Assume that the man has a mass of 80 kg, with a center of gravity 1.0 mabove the ground. The action of the wind on his torso, which we approximate as a cylinder 50 cmwide and 90 cm long centered 1.2...

A person with mass m1 = 80 kg person climbs a uniform ladder with mass m2...

A person with mass m1 = 80 kg person climbs a uniform ladder with mass m2 = 40 kg and length L = 10 m long that rests against a vertical frictionless wall at an angle of θ = 70° with the floor. When the person climbs 7.0 m from the base of the ladder, the ladder starts to slip. When answering the questions, use the symbolic notations given before using numerical substitutions. B)Find the force of the wall Fw...

Question