A waiter carries a 253g drink a distance of 12m on a horizontal tray at constant speed of 1.1 m/s.

A) what work is done by the normal force of the tray on the drink?
B) what work is done by the friction force of the tray on the drink?

To find the work done by different forces on the drink, we need to understand the concepts of work and the forces acting on the drink.

A) Work done by the normal force of the tray on the drink:
The normal force is the force exerted by a surface perpendicular to the object resting on it. In this case, the tray exerts a normal force on the drink to counteract the weight of the drink.

The formula to calculate work is: Work = Force * Distance * cos(theta),
where:
- Work is the amount of energy transferred by a force.
- Force is the magnitude of the force applied.
- Distance is the distance over which the force is applied.
- theta is the angle between the force and the direction of motion (cos(theta) is 1 when the force and displacement are in the same direction).

In this case, since the tray is horizontal, the angle theta is 0 degrees, and cos(theta) = 1. So, the formula reduces to: Work = Force * Distance.

The normal force of the tray on the drink is equal in magnitude and opposite in direction to the weight of the drink. The weight of an object can be calculated using the formula: Weight = mass * gravitational acceleration.
Given that the mass of the drink is 253g (0.253kg) and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the weight of the drink.

Weight = 0.253kg * 9.8 m/s^2 = 2.4814 N.

Therefore, the work done by the normal force is: Work = Force * Distance = 2.4814 N * 12m = 29.777 N·m or 29.77 J (Joules).

B) Work done by the friction force of the tray on the drink:
Friction is the force that opposes the relative motion of two surfaces in contact. In this case, the friction force acts between the tray and the drink, preventing the drink from sliding off the tray.

Since the drink moves at a constant speed, we know that the net force acting on it is zero. Therefore, the force of friction must be equal in magnitude and opposite in direction to the normal force.

The work done by the friction force can be calculated using the same formula as before: Work = Force * Distance.
Since the friction force and the displacement are in opposite directions, the angle theta is 180 degrees, and cos(theta) = -1.

The work done by the friction force is: Work = Force * Distance * cos(theta) = -Force * Distance.

Using the weight of the drink as the magnitude of the force, we can find the work done by the friction force:

Work = -Force * Distance = -2.4814 N * 12m = -29.777 N·m or -29.77 J (Joules).

Therefore, the absolute value of the work done by the friction force is 29.77 J, but the negative sign indicates that the friction force opposes the displacement of the drink.