BIO The Kinetic Energy of Walking. If a person of mass M simply moved forward with speed V , his kinetic energy would be 1 2 MV 2 . However, in addition to possessing a forward motion, various parts of his body (such as the arms and legs) undergo rotation. Therefore, his total kinetic energy is the sum of the energy from his forward motion plus the rotational kinetic energy of his arms and legs. The purpose of this problem is to see how much this rotational motion contributes to the person’s kinetic energy. Biomedical measurements show that the arms and hands together typically make up 13% of a person’s mass, while the legs and feet together account for 37%. For a rough (but reasonable) calculation, we can model the arms and legs as thin uniform bars pivoting about the shoulder and hip, respectively. In a brisk walk, the arms and legs each move through an angle of about ±30° (a total of 60°) from the vertical in approximately 1 second. Assume that they are held straight, rather than being bent, which is not quite true. Consider a 75-kg person walking at 5.0 km/h. having arms 70 cm long and legs 90 cm long. (a) What is the average angular velocity of his arms and legs? (b) Using the average angular velocity from part (a), calculate the amount of rotational kinetic energy in this person’s arms and legs as he walks, (c) What is the total kinetic energy due to both his forward motion and his rotation? (d) What percentage of his kinetic energy is due to the rotation of his legs and arms?
BIO The Kinetic Energy of Walking. If a person of mass M simply moved forward with speed V , his kinetic energy would be 1 2 MV 2 . However, in addition to possessing a forward motion, various parts of his body (such as the arms and legs) undergo rotation. Therefore, his total kinetic energy is the sum of the energy from his forward motion plus the rotational kinetic energy of his arms and legs. The purpose of this problem is to see how much this rotational motion contributes to the person’s kinetic energy. Biomedical measurements show that the arms and hands together typically make up 13% of a person’s mass, while the legs and feet together account for 37%. For a rough (but reasonable) calculation, we can model the arms and legs as thin uniform bars pivoting about the shoulder and hip, respectively. In a brisk walk, the arms and legs each move through an angle of about ±30° (a total of 60°) from the vertical in approximately 1 second. Assume that they are held straight, rather than being bent, which is not quite true. Consider a 75-kg person walking at 5.0 km/h. having arms 70 cm long and legs 90 cm long. (a) What is the average angular velocity of his arms and legs? (b) Using the average angular velocity from part (a), calculate the amount of rotational kinetic energy in this person’s arms and legs as he walks, (c) What is the total kinetic energy due to both his forward motion and his rotation? (d) What percentage of his kinetic energy is due to the rotation of his legs and arms?
BIO The Kinetic Energy of Walking. If a person of mass M simply moved forward with speed V, his kinetic energy would be
1
2
MV2. However, in addition to possessing a forward motion, various parts of his body (such as the arms and legs) undergo rotation. Therefore, his total kinetic energy is the sum of the energy from his forward motion plus the rotational kinetic energy of his arms and legs. The purpose of this problem is to see how much this rotational motion contributes to the person’s kinetic energy. Biomedical measurements show that the arms and hands together typically make up 13% of a person’s mass, while the legs and feet together account for 37%. For a rough (but reasonable) calculation, we can model the arms and legs as thin uniform bars pivoting about the shoulder and hip, respectively. In a brisk walk, the arms and legs each move through an angle of about ±30° (a total of 60°) from the vertical in approximately 1 second. Assume that they are held straight, rather than being bent, which is not quite true. Consider a 75-kg person walking at 5.0 km/h. having arms 70 cm long and legs 90 cm long. (a) What is the average angular velocity of his arms and legs? (b) Using the average angular velocity from part (a), calculate the amount of rotational kinetic energy in this person’s arms and legs as he walks, (c) What is the total kinetic energy due to both his forward motion and his rotation? (d) What percentage of his kinetic energy is due to the rotation of his legs and arms?
Definition Definition Rate of change of angular displacement. Angular velocity indicates how fast an object is rotating. It is a vector quantity and has both magnitude and direction. The magnitude of angular velocity is represented by the length of the vector and the direction of angular velocity is represented by the right-hand thumb rule. It is generally represented by ω.
A cart on wheels (assume frictionless) with a mass of 20 kg is pulled rightward with a 50N force. What is its acceleration?
Two-point charges of 5.00 µC and -3.00 µC are placed 0.250 m apart.a) What is the electric force on each charge? Include strength and direction and a sketch.b) What would be the magnitude of the force if both charges are positive? How about the direction?
c) What will happen to the electric force on each piece of charge if they are moved twice as far apart? (Give a numerical answer as well as an explanation.)
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