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- A small block of mass m = 200 g is released from rest at point along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 30.0 cm (Fig. P7.45). Calculate (a) the gravitational potential energy of the block-Earth system when the block is at point relative to point . (b) the kinetic energy of the block at point , (c) its speed at point , and (d) its kinetic energy and the potential energy when the block is at point . Figure P7.45 Problems 45 and 46.An inclined plane of angle = 20.0 has a spring of force constant k = 500 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in Figure P6.61. A block of mass m = 2.50 kg is placed on the plane at a distance d = 0.300 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest?An astronaut lands on a newly-discovered planet (without an atmosphere). As an experiment, she throws vertically upwards a pure vanadium sphere of radius 2.0 cm and density 5.5 × 103 kg m-3 with an initial speed of 3.0 m s-¹. The point of release is 1.2 m above the ground. She observes the sphere to travel 4.8 m before it starts falling to the ground. Calculate the kinetic energy of the projectile just as it hits the ground. Kinetic energy = J.
- A smooth circular hoop with a radius of 0.900 m is placed flat on the floor. A 0.475-kg particle slides around the inside edge of the hoop. The particle is given an initial speed of 9.00 m/s. After one revolution, its speed has dropped to 5.00 m/s because of friction with the floor. (a) Find the energy transformed from mechanical to internal in the particle-hoop-floor system as a result of friction in one revolution. 13.3 (b) What is the total number of revolutions the particle makes before stopping? Assume the friction force remains constant during the entire motion. 1 Your response differs from the correct answer by more than 10%. Double check your calculations. revAn astronaut lands on a newly-discovered planet (without an atmosphere). As an experiment, she throws vertically upwards a pure vanadium sphere of radius 2.0 cm and density 5.5 × 103 kg m3 with an initial speed of 3.0 ms 1. The point of release is 1.2 m above the ground. She observes the sphere to travel 4.8 m before it starts falling to the ground. Calculate the kinetic energy of the projectile just as it hits the ground.of a copper wire of uniform cross section and Ex. 70: find the energy stored per unit volume of length 1.5 m, when it is stretched to a length of a copper wire of uniform cross section and of length 1.5 m, when it is stretched to length a of 1.51 m by a stress of 3 x 102 N/m2.
- A windmill for the generation of electric power has a propeller of diameter 1.8 m. In a wind of 40 km/h, this windmill delivers 200 W of electric power. (a) At this wind speed, what is the rate at which the air carries kinetic energy through the circular area swept out by the propeller? (The density of air is 1.29 kg/m3). (b) What percentage of the kinetic energy of the air passing through this area is converted into electric energy?(a) Which component of the horizontal axis wind turbine can be considered as the brain of the system? Write the important functions of this component. Explain how it coordinates with the anemometer, wind vane and yaw drive for the proper working of turbine. I (b) Explain, why wind energy is considered as highly desirable and economical to the rural areas which are far from existing gridsA smooth circular hoop with a radius of 0.500 m is placed flat on the floor. A 0.400-kg particle slides around the inside edge of the hoop. The particle is given an initial speed of 8.00 m/s. After one revolution, its speed has dropped to 6.00 m/s because of friction with the floor. (a) Find the energy transformed from mechanical to internal in the particle–hoop–floor system as a result of friction in one revolution. (b) What is the total number of revolutions the particle makes before stopping? Assume the friction force remains constant during the entire motion.
- A device used for mixing consists of three identical thin rods extending from a central axle, all in the same plane, and spaced apart from each other by 120°. Each rod is 10.4 cm long, and attached to the end of each rod is a ball with a cross-sectional area 4.50 cm2. Each ball has a drag coefficient of 0.520. A motor drives the central axle, causing the device to rotate. (a) How much power (in W) must be supplied by the motor for the device to rotate at a constant speed of 1000 rev/min in air? (Use 1.20 kg/m3 for the density of air at 20°C.) 0.532 What is the force of air resistance, and what does it depend on? What torque does this force apply? How is power related to torque and angular speed? How is linear speed related to angular speed? RememberArteriosclerotic plaques forming on the inner wall of arteries can decrease the effective cross-sectional area of an artery. Even small changes in the effective area of an artery can lead to very large changes in the blood pressure in the artery and possibly to the collapse of the blood vessel. Imagine a healthy artery, with blood flow velocity of vo equals 0.14 m/s and mass per volume of p = 1050 kg/m³. The kinetic energy per unit volume of blood is given pv². This is one of the terms in Bernoulli's equation. Imagine that plague has narrowed an artery to 1/10 of its normal cross-sectional area, a 90% blockage. 1 2 by ko = a) Compared to normal blood flow velocity, vo, what is the velocity of blood as it passes through this blockage? b) By what factor does the kinetic energy per unit of blood volume change as the blood passes through this blockage? c) Using Bernoulli's equation as the blood passes through this blockage, what happens to the blood pressure?A device used for mixing consists of three identical thin rods extending from a central axle, all in the same plane, and spaced apart from each other by 120°. Each rod is 10.6 cm long, and attached to the end of each rod is a ball with a cross-sectional area 4.10 cm2. Each ball has a drag coefficient of 0.660. A motor drives the central axle, causing the device to rotate. (a) How much power (in W) must be supplied by the motor for the device to rotate at a constant speed of 1000 rev/min in air? (Use 1.20 kg/m3 for the density of air at 20°C.) W (b) How much power (in W) must be supplied by the motor for the device to rotate at a constant speed of 1000 rev/min in water? (The density of water is 1.00 g/cm³, or 1,000 kg/m3.) W