Question

Consider a horizontal forearm. On one end of the forearm is the elbow, and on the other end is the hand. The forearm has a mass of 1.01 kg. The distance from the elbow to the hand is 41.7 cm. If the biceps muscle connects to the forearm a distance of 5.81 cm from a the elbow, and the biceps muscle can supply a maximum force of 664. N (with the forearm ina horizontal position), what is the maximum mass (in kg) that the person can bold?

Answer 1

The maximum mass a person can hold depends on the force exerted by the biceps muscle and the torque created around the elbow joint. In this scenario, the maximum mass that can be held is approximately 10.03 kg.

Step-by-step explanation:

The maximum mass that a person can hold depends on the force exerted by the biceps muscle and the torque created around the elbow joint. In this scenario, the biceps muscle can supply a maximum force of 664 N when the forearm is in a horizontal position. To calculate the maximum mass, we need to find the torque created by this force at the elbow joint.

The torque can be calculated as the product of the force and the perpendicular distance from the force to the fulcrum. In this case, the force is acting at a distance of 5.81 cm from the elbow and the forearm has a mass of 1.01 kg. The distance from the elbow to the hand is 41.7 cm.

Using the equation for torque, T = F * d, we can calculate the torque:

T = 664 N * 0.0581 m = 38.5484 N*m

Now, we can calculate the maximum mass that can be held by rearranging the torque equation:

M = T / (g * r), where M is the maximum mass, g is the acceleration due to gravity (9.8 m/s^2), and r is the distance from the elbow to the center of mass of the forearm and hand. In this case, r = 0.417 m.

Plugging in the values, we get:

M = 38.5484 N*m / (9.8 m/s^2 * 0.417 m) ≈ 10.03 kg

Answer 2

The maximum mass that a person can hold can be calculated using the concept of torque. Applying this concept, we find that the maximum mass that can be held is approximately 10.721 kg.

Step-by-step explanation:

The maximum mass that a person can hold can be calculated using the concept of torque. Torque is the product of the force applied and the distance from the point of rotation or pivot. In this case, the pivot is the elbow and the force is applied by the biceps muscle connecting to the forearm.

Since the biceps muscle can supply a maximum force of 664 N and the distance from the elbow to the biceps muscle connection is 5.81 cm, we can calculate the torque exerted by the biceps muscle as: Torque = Force * Distance = (664 N) * (0.0581 m) = 38.5324 Nm

To find the maximum mass that can be held, we need to consider the torque exerted by the weight of the forearm and hand. The weight of the forearm and hand can be calculated as the product of their mass and the acceleration due to gravity (9.8 m/s^2). The distance from the elbow to the center of mass of the forearm and hand is 41.7 cm, which can be converted to meters as 0.417 m.

Let's assume the maximum mass that can be held is M kg. The torque exerted by the weight is then given by: Torque = Weight * Distance = (M kg * 9.8 m/s^2) * (0.417 m)

Since the forearm is in a horizontal position, the torque exerted by the weight should be equal to or less than the torque exerted by the biceps muscle. Therefore, we can set up the following inequality:

38.5324 Nm ≥ (M kg * 9.8 m/s^2) * (0.417 m)

Simplifying the inequality, we get:

M ≤ 38.5324 Nm / (9.8 m/s^2 * 0.417 m)

Solving for M, the maximum mass that can be held is approximately 10.721 kg.