You have been hired as part of a team to design a mechanical arm as a model for future prosthetics. To begin the project you evaluate several simple designs that test specific features needed in the final device. The first is designed for lifting small objects. The arm is a steel bar of uniform thickness with one end attached to the base by a hinge (elbow) that allows it to rotate in the vertical plane. Near the other end of the arm is a cable that supports a small weight. The arm is supported at an angle to the horizontal by another cable, intended to mimic a bicep muscle. One end of the support cable is attached to the arm and the other end goes over a pulley. That other end is attached to a counterweight that hangs straight down. The pulley is supported by a mechanism that adjusts its height so the support cable is always horizontal. Your task is to determine how the attachment point of the lifting cable varies as a function of the mass of the object being lifted in order to hold the bar steady. The mass of the arm, the mass of the counterweight, the attachment point of the support cable and the attachment point of the lifting cable have all been specified for your model. In essence you want your arm to "balance," with the lifted object held steady. Beginning with basic physics principles, show how you get an equation that gives the attachment point of the lifting cable of the apparatus.
You have been hired as part of a team to design a mechanical arm as a model for future prosthetics. To begin the project you evaluate several simple designs that test specific features needed in the final device. The first is designed for lifting small objects. The arm is a steel bar of uniform thickness with one end attached to the base by a hinge (elbow) that allows it to rotate in the vertical plane. Near the other end of the arm is a cable that supports a small weight. The arm is supported at an angle to the horizontal by another cable, intended to mimic a bicep muscle. One end of the support cable is attached to the arm and the other end goes over a pulley. That other end is attached to a counterweight that hangs straight down. The pulley is supported by a mechanism that adjusts its height so the support cable is always horizontal. Your task is to determine how the attachment point of the lifting cable varies as a function of the mass of the object being lifted in order to hold the bar steady. The mass of the arm, the mass of the counterweight, the attachment point of the support cable and the attachment point of the lifting cable have all been specified for your model. In essence you want your arm to "balance," with the lifted object held steady. Beginning with basic physics principles, show how you get an equation that gives the attachment point of the lifting cable of the apparatus.
