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2) Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industria flywheel has a 1.5 m diameter and a mass of 250 kg. Its maximum angular velocity is 1200 rpm. a. A motor spins up the flywheel with a constant torque of 50Nm. How long does it take the flywheel to reach top speed? b. How much energy is stored in the flywheel?
2008 2008 B 10 cm 3) The tour masses shown in figure are connected by massless, rigid rods. a. Find the coordinates of the center of mass. b. Find the moment of inertia about an axis that is perpendicular to the page and runs through the (1) center of mass. (l) object D c Find the moment of inertia about an axis that passes through objects and D. 10 cm A 100 2008
4) The three 200 g masses in figure are connected by massless, rigid rods. a. Find the coordinates of center of mass. b. What is the triangle's moment of inertia about the axis through the center? c. What is the triangle's kinetic energy if it rotates about the axis at 5.0 rev/s ? ZA 40 cm 40 cm Axis 602 40 cm
5) An athlete at the gym holds a 3.0 kg steel ball in his hand. His arm is 70 cm long and has a mass of 3.8 kg, with the center of mass at 50% of the arm length from the shoulder (a) What is the magnitude of the torque about his shoulder due to the weight of the ball and his arm if he holds his arm straight out to his side, parallel to the floor? (b) What is the magnitude of the torque about his shoulder due to the weight of the ball and his arm if he holds his arm straight, but 45. below horizontal?
6) Weightlifting can exert extremely large forces on the body's joints and tendons. In the strict curl event, a standing athlete uses both arms to lift a barbell by moving only his forearms, which pivot at the elbows. The record weight lifted in the strict curl is over 200 pounds (about 900 N). Figure shows the arm bones and the biceps, the main lifting muscle when the forearm is horizontal. What is the tension in the tendon connecting the biceps muscle to the bone while a 900 N barbell is held stationary in this position? Lifting muscle (biceps) 4.0 cm 35 cm
7) A 120-cm-wide sign hangs from a 5.0 kg, 200-cm-long pole. A cable of negligible mass supports the end of the rod as shown in figure. What is the maximum mass of the sign if the maximum tension in the cable without breaking is 300 N? Cable 250 cm 200 cm PITSILI 18!?!
8) An 80kg construction worker sits down 2.0m from the end of a 1450kg steel beam to eat his lunch, as shown in the figure. The cable supporting the beam is rated at 15000N. Should the worker be worried? Cable 300 6.0 m
Q9) An 8.0-cm-diameter, 400 g solid sphere is released from rest at the top of a 2.1-m-long, 25° incline. It rolls, without slipping, to the bottom a. What is the sphere's angular velocity at the bottom of the incline? b. What fraction of its kinetic energy is rotational?
Q10) Luc, who is 1.80 m tall and weighs 950 N, is standing at the center of a playground merry-go-round with his arms extended, holding a 4.0 kg dumbbell in each hand. The merry-go-round can be modeled as a 4.0-m-diameter disk with a weight of 1500 N. Luc's body can be modeled as a uniform 40-cm-diameter cylinder with massless arms extending to hands that are 85 cm from his center. The merry-go-round is coasting at a steady 35 rpm when Luc brings his hands in to his chest. Afterward, what is the angular velocity, in rpm, of the merry-go-round?
X 11) The International Space Station is orbiting at an altitude of about 370 km above the earth's surface. The mass of the earth is 5.97 x 1024 kg, the radius of the earth is 6.38 x 106 m, and G = 6.67 x 10-11 N m2/kg2 Assuming a circular orbit, (a) what is the period of the International Space Station's orbit? th) what is the speed of the International Space Station in its orbit?
12) A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. (a) What is the maximum speed of the needle? (b) What is the maximum acceleration of the needle?
12) A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. (a) What is the maximum speed of the needle? (b) What is the maximum acceleration of the needle?
13) Astronauts on the first trip to Mars take along a pendulum whose period on earth is 1.50 s. The period on Mars turns out to be 2.45 s. What is the free fall acceleration on the mars?
14) A 3.0-m-tall, 50-cm-diameter concrete column supports a 200,000 kg load. By how much is the column compressed?
15) A steel guitar string with a diameter of 0.300 mm and a length of 70.0 cm is stretched by 0.500 mm while being tuned. How much force is needed to stretch the string by this amount? Young's modulus for steel is 20 x 1011 N/m2