The forearm is used to accelerate a 1.2 kg ball by using the triceps muscle as shown in the figure. The forearm has a mass of 3.7 kg and rotates like a uniform rod about an axis at one end. The ball is accelerated uniformly from rest to 9.0 m/s in a time of 0.45 s, when it is released. Part A Calculate the angular acceleration of the arm. Part B Calculate the force that the triceps muscle must exert to provide the necessary acceleration in part A.
The forearm is used to accelerate a 1.2 kg ball by using the triceps muscle as shown in the figure. The forearm has a mass of 3.7 kg and rotates like a uniform rod about an axis at one end. The ball is accelerated uniformly from rest to 9.0 m/s in a time of 0.45 s, when it is released. Part A Calculate the angular acceleration of the arm. Part B Calculate the force that the triceps muscle must exert to provide the necessary acceleration in part A.
The forearm is used to accelerate a 1.2 kg ball by using the triceps muscle as shown in the figure. The forearm has a mass of 3.7 kg and rotates like a uniform rod about an axis at one end. The ball is accelerated uniformly from rest to 9.0 m/s in a time of 0.45 s, when it is released. Part A Calculate the angular acceleration of the arm. Part B Calculate the force that the triceps muscle must exert to provide the necessary acceleration in part A.
The forearm is used to accelerate a 1.2 kg ball by using the triceps muscle as shown in the figure. The forearm has a mass of 3.7 kg and rotates like a uniform rod about an axis at one end. The ball is accelerated uniformly from rest to 9.0 m/s in a time of 0.45 s, when it is released.
Part A
Calculate the angular acceleration of the arm.
Part B
Calculate the force that the triceps muscle must exert to provide the necessary acceleration in part A.
Transcribed Image Text:The image illustrates the anatomy and mechanics of the human arm, specifically focusing on the elbow joint and the triceps muscle. The key features labeled in the image include:
1. **Axis of Rotation (at elbow)**: This is the pivot point around which the forearm rotates when the elbow is extended or flexed. The axis is located at the elbow joint.
2. **Triceps Muscle**: This is a large muscle on the back of the upper limb responsible for the extension of the elbow joint. It is shown in the image running along the back of the upper arm.
3. **Dimensions**:
- The distance from the axis of rotation at the elbow to the point of force application (in this case, the hand) is labeled as 31 cm.
- The distance from the axis of rotation to where the triceps muscle attaches is 2.5 cm.
The diagram helps to visualize how the triceps muscle creates a lever system which allows for arm movement. The distances indicated provide a clearer understanding of the muscle attachment points relative to the joint and how leverage is applied during arm motion.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
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