A person walks around in circles He starts from 10 meters y = 0, to x = 0 y = 10

Question

A person walks around in circles He starts from 10 meters y = 0, to x = 0 y = 10m, then x = -10m y = 0, and then x = 0, y = 1 10m, and back to x = 10m, y = 0, and going on around and around in constant 4 minutes for each round trip. a) What is the period of the circular motion? _____ b) What is tangential velocity around the circle at theta = 45 degree from the starting point _____ c) What is the angular speed of the circular motion _____ d) At the location 10m and y = 0, what is his velocity? A disk rolls along the ground with linear speed of 3 m/sec as measured at its geometric center. The radius of the disk is 10 cm. a) Where is the instantaneous center of rotation? b) What is the instantaneous linear velocity of the bottom of the disk? c) What is the instantaneous velocity of the top of the disk? d) What the angular speed measured at the center of the disk? A hammer can be used to pill nail out of a wood, as shown in the following figure. The handle bar of the hammer is of 10 inches long and the hook of the hammer is 1 inch long, The nail is held by wood with 200 lb. force. Find the minimal force on the handle bar to pull the mail. a) What is the torque about the end of the hammer as a rotation point, which is created by the nail in rotating the hammer? _____ b) What is the force applied on the end of handle to create a torque that is in equilibrium with the nail's torque? _____ Draw the force on the left figure. A ladder weights of 25 lb. and is of 20 feet long. It is held against the smooth wall at 60 degree at lower end on the ground. Find the force needed on the lower end to make the ladder in equilibrium. a) What is the normal force on the lower end of the ladder? Equation _____ b) What is the torque about the top of the ladder, created by the normal force up and weight downward? Equation: c) The torque created by the horizontal component of the force has to be in equilibrium with the torqued in (b). Set up this equation and find the horizontal force. Equation: d) Draw the directions for the torque in (b) and torque in (a). Find the greatest speed to make a safe right turn without rolling over as shown in the following figure.

Explanation / Answer

As the person takes 4 minutes for every round trip so time period is 4 minute = 240 second.

Since he is moving with constant speed and this speed v = 2*pi*r/240 = 0.262 m/s. So his tangential speed at required point is 0.262 m/s.

Angular speed = v/R = 0.262/10 = 0.0262 rad/s.

At location x=10 m and y=0 m, the velocity of the person is 0.262 m/s along positive y direction.

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