two cats are sitting on a seesaw which is a 3-metre long wooden plank weighing 2kg. the cat on the right is 0.5m from the pivot point and has a mass of 12kg. The cat on the left is 1.3m from the left and of the plank as shown in the figure. Calculate the mass of the cat sitting on the left side if the plank remains horizontal.

I guess the pivot point is at the center, 1.5 from left?

if so
cat on left is 1.5 -1.3 = .2 from pivot
cat on right is at .5 from pivot
plank weight is at pivot
so
m * .2 = 12*.5
m = 6/.2 = 30 kg

d1 = 0.5 m.

M1 = 12kg.

d2 = 1.5 - 1.3 = = 0.2 m.
M2 = ?

M1*d1 = M2*d2.
12 * 0.5 = M2 * 0.2,
M2 = ?

m

To calculate the mass of the cat sitting on the left side, we can use the principle of moments.

The principle of moments states that for an object to be in equilibrium (not rotating), the sum of the anticlockwise moments must be equal to the sum of the clockwise moments.

In this case, the moments can be calculated by multiplying the distance from the pivot point to the weight by the weight itself.

First, let's find the moment of the wooden plank:

Moment of the wooden plank = distance from pivot point to the weight of the wooden plank x weight of the wooden plank
Moment of the wooden plank = 1.3 m x 2 kg = 2.6 kgm

Next, let's find the moment of the cat on the right side:

Moment of the cat on the right = distance from pivot point to the cat on the right x weight of the cat on the right
Moment of the cat on the right = 0.5 m x 12 kg = 6 kgm

Now, to keep the plank horizontal (in equilibrium), the sum of the anticlockwise moments must be equal to the sum of the clockwise moments.

Clockwise moment = moment of the cat on the right
Anticlockwise moment = moment of the wooden plank + moment of the cat on the left

Since the total sum of moments must be zero for equilibrium:
6 kgm = 2.6 kgm + moment of the cat on the left

Simplifying the equation:
moment of the cat on the left = 6 kgm - 2.6 kgm
moment of the cat on the left = 3.4 kgm

Finally, to find the mass of the cat on the left side, divide the moment of the cat on the left by its distance from the pivot point:

Mass of the cat on the left = moment of the cat on the left / distance from pivot point to the cat on the left
Mass of the cat on the left = 3.4 kgm / 1.3 m
Mass of the cat on the left ≈ 2.62 kg

Therefore, the approximated mass of the cat sitting on the left side is 2.62 kg.