A cook holds a 2.66-kg carton of milk at arm's length (see the figure below). What force B must be exerted by the biceps muscle? (Ignore the weight of the forearm. State the magnitude of the force B.)
To determine the force B exerted by the biceps muscle, we need to consider the weight of the carton of milk.
The weight of an object can be calculated using the formula:
Weight = mass x gravitational acceleration
Given:
Mass of the carton of milk (m) = 2.66 kg
Gravitational acceleration (g) = 9.8 m/s^2 (approximate value on Earth)
Now, we can calculate the weight of the carton of milk using the formula:
Weight = 2.66 kg x 9.8 m/s^2
= 26.068 N (Newtons)
Therefore, the force B exerted by the biceps muscle is approximately 26.068 N.
To determine the force B that must be exerted by the biceps muscle, we need to consider the equilibrium of forces acting on the carton of milk.
In this case, we have two forces acting on the carton of milk:
1. The weight of the carton of milk, which can be calculated as the product of its mass (2.66 kg) and the acceleration due to gravity (9.8 m/s^2).
Weight = mass * acceleration due to gravity
2. The force B exerted by the biceps muscle.
Since the carton of milk is at rest and held at arm's length, the net force acting on it must be zero (equilibrium condition). Therefore, the force B exerted by the biceps muscle must balance the weight of the carton.
Mathematically, we can express this equilibrium condition as:
B - Weight = 0
Rearranging the equation to solve for B:
B = Weight
Substituting the given values:
Weight = mass * acceleration due to gravity
Weight = 2.66 kg * 9.8 m/s^2
Calculating the weight:
Weight = 26.068 N (Newtons)
Therefore, the magnitude of the force B that must be exerted by the biceps muscle is approximately 26.068 N.
The answer depends upon the arm's length and another dimension separating the bicep from the rotator cuff. These dimensions should have been on the "figure below" that you did not provide.
The weight of the arm itself should add to the stress force required to support the milk carton.
A figure with the missing dimensions that you need, and the method of solution, can be found on page 142 of this web site:
http://physics.ucsd.edu/students/courses/summer2009/session1/managed/session1/physics1a/documents/ch_8_solutions.pdf