A uranium-238 nucleus undergoes a radioactive decay, 238 U 234Th + 4He. The masses are approximately 238, 234 and 4 u, where u = the atomic mass unit. The U nucleus is initially at rest. Suppose the He nucleus has speed v. Then what is the kinetic energy of the Th nucleus? Parameters: u = 1.66 x 10-27 kg; v = 9.000×106 m/s. (in J)
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- A 3.00 kgkg mass is pushed against a horizontal spring of force constant 28.0 N/cmN/cm on a frictionless air table. The spring is attached to the tabletop, and the mass is not attached to the spring in any way. When the spring has been compressed enough to store 12.5 JJ of potential energy in it, the mass is suddenly released from rest. Find the greatest speed the mass reaches. Express your answer in meters per second. What is the greatest acceleration of the mass? Express your answer in meters per square second.39. 40. 41. In moving an object 7.0 m, 40 J of energy are expended. The average force exerted is closest to (a) 2.8 x 10² N (b) 47 N (c) 28 N (d) 5.7 N (e) 0.18 N A bullet is fired from a gun with a speed of 1000 cm/s. If the bullet has a mass of 0.01 kg, it possesses a kinetic energy of (a) 0.05 J (b) 0.5 J (c) 1 J (d) 5 J (e) 5 x 10³ J Mr. Brady takes the elevator out side his office. The elevator is rising at a constant velocity. Consider these statements concerning the elevator. 1) The upward force in the supporting cable is of constant magnitude. The kinetic energy of the elevator is constant. Its gravitational potential energy is constant. Its acceleration is zero. The sum of its kinetic energy and its gravitational potential energy is constant. Which one of the following groups contains true statements only? (a) I, II, III, IV, and V (b) II and V only (c) IV and V only (d) I, II, and III only (e) I, II and IV onlyTwo masses are pressed against opposite ends of a spring, with one mass at either end of the spring. The spring is has a spring constant of 181 N/m and the two 0.200 kg masses are identical to each other. Pressing the masses against the ends of the spring compresses the spring 21.5 cm from its normal length. If both masses rest on a frictionless, horizontal table, find the speed of each mass in SI units when it has moved free of the spring on the table.
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- Two different masses are sitting on a frictionless track with a compressed spring between them which has 4.0 J of potential energy. When released, the spring pushes the masses apart. If one mass is 2.0 kg and the other mass is 5.0 kg, what is the speed of each mass after the spring stops pushing them apart? Assume the mass of the spring is negligible.Consider three vectors A = 13.1i + 3.9j, B = 8.9i + 9.1j, and C = -2.1i - 16.8j. Part (a) What is the result of 2A⋅(B - 3C)? Part (b) What is the result of A⋅A + B⋅B + C⋅C?A proton (mass m = 1.67 × 10-27 kg) is being accelerated along a straight line at 6.20 x 10¹1 m/s² in a machine. If the proton has an initial speed of 8.50 x 104 m/s and travels 2.10 cm, what then is (a) its speed and (b) the increase in its kinetic energy? (a) Number (b) Number i Units Units
- Under normal conditions the human heart converts about 12.7 J of chemical energy per second into 1.27 W of mechanical power as it pumps blood throughout the body HINT (a) Determine the number of Calories required to power the heart for one day, given that 1 Calorie equals 4186 J. Cal (b) Metabolizing 1 kg of fat can release about 9000 Calories of energy. What mass of metabolized fat (in kg) would power the heart for one day? kg Need Help? Watch it Read ItIf a particle is moving, it has kinetic energy. Kinetic energy is the energy of motion, and it depends on the speed and mass of the particle. It is given by the formula Ek = 1/2*mv2, where Ek is the kinetic energy, m is the mass, and v is the speed of the particle. The formula for kinetic energy has some important features to keep in mind. Kinetic energy, and every other type of energy as well, is a scalar quantity, given by only a single number. Energy does not have a "direction", unlike a vector quantity. (This is in contrast to the vector quantity momentum, which you might have already studied.) Kinetic energy, in particular, is always a positive number. (Note the speed v is the magnitude of the vector velocity, and therefore is positive. But even if it were a negative number, squaring it would always lead to a positive result.) Kinetic energy depends on the square of the speed. (This is in contrast to the magnitude of momentum, mv, a quantity you may have already studied, which…The kinetic energy of a mass moving in the x-y plane is: T = mx² + my² Using the transformation = rcos (0) and y = rsin (0), derive a general expression for kinetic energy of the mass in the r, basis.