Question

A student of mass 51 kg wants to walkbeyond the edge of a cliff on a heavy beam ofmass 220 kg and length 11 m. The beam isnot attached to the cliff in any way, it simplylies on the horizontal surface of the clifftop,with one end sticking out beyond the cliff’sedgeHow far from the edge of the ledge can the beam extend if it sticks out as far as possible beyond the edge, but the student can walk to the beam’s end without falling down? Answer in units of m.

Answer 1

Answer:

4.465 m

Explanation:

Taken the beam to be uniform, then the center of gravity will act at the mid-point of the beam. The mid point = 11 / 2 = 5.5 m

since the boy can walk to the end of the beam without falling,

then the torque ( moment of the force) by beam = torque by students at the end of the beam

let the distance of the boy = x

220 ( 5.5 - x ) = 51 × x

1210 - 220 x = 51 x

1210 = 51 x + 220 x

1210 = 271 x

x = 1210 / 271 = 4.465 m

Answer 2

The distance from the edge of the ledge can the beam extend if it sticks out as far as possible beyond the edge, but the student can walk to the beam’s end without falling down will be x=4.465 m

What is torque?

Torque is a measure of the force that can cause an object to rotate about an axis. Just as force is what causes an object to accelerate in linear kinematics, torque is what causes an object to acquire angular acceleration

Taken the beam to be uniform, then the center of gravity will act at the mid-point of the beam. The mid point = 11 / 2 = 5.5 m

since the boy can walk to the end of the beam without falling,

then the torque ( moment of the force) by beam = torque by students at the end of the beam

let the distance of the boy = x

220 ( 5.5 - x ) = 51 × x

1210 - 220 x = 51 x

1210 = 51 x + 220 x

1210 = 271 x

$x = \dfrac{ 1210} { 271} = 4.465 m$

Hence the distance will be x=4.465 m

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