Question

Jack and jill have masses of 45 kg and 32 kg respectively. both are balanced on opposite ends of a 5.0 m long wooden plank with a mass of 16 kg. at what point along the plank does the pivot point have to be?

Answer 1

2.15m

Step-by-step explanation:

Assume the plank has uniform mass, then the total mass of 16 kg can be simplified as a point weight at its center, aka position 2.5m.

Let's Jack and Jill positions are at 0 and 5 m, respectively. And the pivot point at position x. We know that Jack is heavier, and so the pivot point is closer to Jack, this way both Jill and plank mass can balance out Jack mass.

Also the distance from Jill to pivot is 5 - x and the distance from plank center to pivot is 2.5 - x.

For the system to balance, the total mass-distance product of (Jill-plank) and Jack should be the same around the pivot:

45x = 32(5-x) + 15(2.5 - x)

45x = 160 - 32x + 37.5 - 15x

92x = 197.5

x = 197.5/92 = 2.15m

So the pivot point is 2.15m from the left

Answer 2

The pivot point have to be placed 1.12m from the 16kg mass which is the mass of the plank

Step-by-step explanation:

This is an equilibrium question. There are three forces acting on the wooden plank, the 45kg, 32kg and 16kg force which is the mass of the plank. Note that the mass of the plank will be placed at the center of the plank.

Therefore our pivot will be placed close towards the 45kg mass to balance the plank.

Using the principle of moments, sum of clockwise moments is equal to the sum of anticlockwise moments. Since Moment = Force×perpendicular distance

Taking moments about the pivot,

If we place the 45kg mass to the left hand side of the pivot and 16kg & 32kg to the right hand side, the 45kg mass will turned anticlockwisely while the the 16kg and 32kg will go in the clockwise direction.

We have;

ACW moment = 45 × (2.5-x)

CW moment for 16kg force = 16 × x

CW moment for 32kg force = 32 × (2..5+x)

Note that the distance between the pivot and the 16kg mass is the unknown variable "x"

45(2.5-x) = 16x + 32(2.5-x)

112.5-45x = 16x + 80-32x

Collecting like terms

112.5-80 = -32x+45x+16x

32.5 = 29x

x = 32.5/29

x = 1.12m

The pivot point have to be placed 1.12m from the 16kg mass which is the mass of the plank.