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

• dtl42
In summary, a uniform round tabletop with a diameter of 4.0 m and a mass of 50.0 kg is supported by evenly spaced legs with a length of 1.0 m and spacing of 3.0 m. The maximum mass of a carpenter that can sit on the edge of the table without toppling it is determined by finding the point at which the normal force exerted by the carpenter lies outside the polygon formed by the legs. The use of torque may be helpful in solving this problem.
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.

#### Attachments

• Diagram.png
1.9 KB · Views: 541
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.

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.

## 1. What does the equation Fnet=ma mean in this context?

The equation Fnet=ma represents Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.

## 2. Why is the maximum mass of the carpenter important for keeping the table upright?

The maximum mass of the carpenter is important because it determines the amount of force that can be applied to the table without causing it to tip over. This is necessary for ensuring the stability and safety of the table.

## 3. How do you calculate the maximum mass of the carpenter?

The maximum mass of the carpenter can be calculated by rearranging the equation Fnet=ma to solve for mass. This gives the formula m=Fnet/a, where Fnet is the maximum force that can be applied to the table without causing it to tip over, and a is the acceleration due to gravity (9.8 m/s^2).

## 4. What factors can affect the maximum mass of the carpenter?

The maximum mass of the carpenter can be affected by several factors, including the strength and stability of the table, the type and distribution of weight on the table, and the friction between the table and the floor.

## 5. How can the maximum mass of the carpenter be increased?

The maximum mass of the carpenter can be increased by increasing the strength and stability of the table, distributing the weight evenly on the table, and minimizing the friction between the table and the floor. Additionally, using materials with a higher strength-to-weight ratio can also increase the maximum mass that the carpenter can support.

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