# Calculating Forces in a Rotating Lunch Tray

• tmurphy12
In summary, the conversation is about a problem involving a lunch tray being held parallel to the ground, with a 1.04-kg plate of food and a 0.248-kg cup of coffee on it. The task is to find the force exerted by the thumb and the four fingers, both of which act perpendicular to the tray. The solution involves drawing a free body diagram, using the facts that the net force and net torque must be zero, and solving for the unknown forces.
tmurphy12
Hello, I know the rules state to show work to receive help but my problem is that i don't know where to begin so i am lookign for a push in the right direction...here is the question...
A lunch tray is being held in one hand, as the figure illustrates. The mass of the tray itself is 0.200 kg, and its center of gravity is located at its geometrical center. On the tray is a 1.04-kg plate of food and a 0.248-kg cup of coffee. Obtain (a) the force exerted by the thumb and (b) the force exerted by the four fingers. Both forces act perpendicular to the tray, which is being held parallel to the ground.
http://edugen.wiley.com/edugen/courses/crs1507/art/qb/qu/c09/ch09p_16.gif
the only thing i did was multiply the masses by gravity to get their weight
again any help would be greatly appreciated.

i also figure that the lever arm will be the length given in the picture...i am just confused as to how to find the force without knowing the torque

Draw a free body diagram for the system... with the two unknown forces they ask for. Then use two facts -- that the net force must be zero, and that the net torque must be zero. Two equations, two unknowns, so you can solve for the unknowns.

## 1. What is rotational dynamics?

Rotational dynamics is a branch of physics that deals with the motion of objects that are rotating or moving in a circular path.

## 2. How is rotational dynamics related to a tray?

A tray can be used as an example to understand rotational dynamics because it undergoes rotational motion when it is rotated by a person's hand.

## 3. What factors affect the rotational dynamics of a tray?

The rotational dynamics of a tray is affected by factors such as the mass of the tray, the force applied on the tray, and the distance of the force from the center of rotation.

## 4. How does the distribution of objects on a tray affect its rotational dynamics?

The distribution of objects on a tray can affect its rotational dynamics by changing its moment of inertia, which is a measure of an object's resistance to rotational motion. Objects placed closer to the center of rotation will have less effect on the tray's rotational dynamics compared to objects placed farther away from the center.

## 5. What is the importance of understanding rotational dynamics of a tray?

Understanding rotational dynamics of a tray can help in designing and improving the stability of serving trays, as well as in analyzing and predicting the motion of objects in circular paths or orbits.

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