Max Mass of Carpenter to Keep Table Upright: Fnet=ma #15

[dtl42]

Homework Statement

A uniform round tabletop of diameter 4.0 m and mass 50.0 kg rests on massless, evenly spaced legs of length 1.0 m and spacing 3.0 m. A carpenter sits on the edge of the table. What is the maximum mass of the carpenter such that the table remains upright? Assume that the force exerted by the carpenter on the table is vertical and at the edge of the table.

Homework Equations

Maybe use torque?

The Attempt at a Solution

I tried using torque to balance it, but it got too messy for me to handle.

 

[tiny-tim]

Hi dtl42!

(i can't see your diagram yet)

Hint: it will topple when the normal force lies outside the polygon defined by the legs.

 

[thomate1]

I would approach this problem by first determining the forces acting on the table. The force of gravity on the tabletop and the carpenter's weight will act downwards, while the normal force from the legs will act upwards. In order for the table to remain upright, the sum of these forces must be equal to zero.

Using Newton's second law, F=ma, we can set up an equation for the vertical forces:

Fnet = Fgravity + Fcarpenter + Flegs = 0

Since the legs are evenly spaced, the normal force from each leg will be equal. We can also assume that the force exerted by the carpenter on the table is equal to their weight. Therefore, the equation becomes:

Fnet = mg + mg + 4N = 0

Solving for the maximum mass of the carpenter, m, we get:

m = -4N / g

Substituting in the values for N (normal force) and g (acceleration due to gravity), we get:

m = -4(50.0 kg)(9.8 m/s^2) / 4 m = -490 kg

This means that the maximum mass of the carpenter that the table can support is 490 kg, assuming that the force exerted by the carpenter on the table is vertical and at the edge of the table. However, this is a negative value, which does not make sense in this context. Therefore, we can conclude that the table cannot support any additional weight and the maximum mass of the carpenter should be considered to be 0 kg.