3. A helical spring of stiffness k is cut into two halves and a mass m is connected to the two halves as shown in (a). The natural time period of this system is found to be 0.5 s. If an identical spring is cut so that one part is one-fourth and the other part three-fourths of the original length, and the mass m is connected to the two parts as shown in (b), what would be the natural period of the system? 00000 (a) (b) A. 0.333 s B. 0.433 s C. 0.533 s D. 0.633 s
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- You are the pilot of a spacecraft intended for travel at very high speeds. Before leaving you measure the spacecraft to be 31.4 m long and have a mass of 5.28 x 104 kg. During your travel, you pass a planet and exchange information with an observer on the planet. You are told that your spacecraft has been measured to be 28.6 m long. a. How fast is your spacecraft travelling with respect to the planet? b. You are told there is a nearby planet that is stationary with respect to the first planet. The observer on the first planet says it will take you 25 s to reach the nearby planet. How far away does your co-pilot on the spacecraft say the nearby planet is? c. How much energy was required to accelerate your spacecraft to this speed?Looking at the following 4-line summary, describe the most significant type of error present in the data. Acceleration due to Gravity (m/s2) Result: 11.2 ± 1.6 Range: 9.6 → 12.8 Theory: 9.8 Agree: yes Looking at the following 4-line summary, describe the most significant type of error present in the data. Acceleration due to Gravity (m/s2) Result: 10.0 ± 0.1 Range: 9.9 → 10.1 Theory: 9.8 Agree: no.A spacecraft cruising in space at a constant velocity of 2000 ft/s has a mass of 25,000 lbm. To slow down the spacecraft, a solid fuel rocket is fired, and the combustion gases leave the rocket at a constant rate of 150 lbm/s at a velocity of 5000 ft/s in the same direction as the spacecraft for a period of 5 s. Assuming the mass of the spacecraft remains constant, determine (a) the deceleration of the spacecraft during this 5-s period, (b) the change of velocity of the spacecraft during this time period, and (c) the thrust exerted on the spacecraft.
- A baseball of mass m= 0.35 kg is spun vertically on a massless string of length L = 0.93 m. The string can only support a tension of Tmax= 10.6 N before it will break. Randomized Variables m = 0.35 kg L = 0.93 m Tmax= 10.6 N Part (a) What is the maximum possible speed of the ball at the top of the loop, in meters per second? Part (b) What is the maximum possible speed of the ball at the bottom of the loop, in meters per second?An astronaut is doing a spacewalk on a long tether at 0.1 km away from the International Space Station (mass of 420,000 kg). His spacesuit includes a very sensitive gravitometer, which indicates the gravitational force acting on the astronaut and his spacesuit from the ISS is 7.0 E−7 N. What is the mass of the astronaut in his suit if G = 6.67 E−11 N*m2/kg2? 1. 150 kg 2. 200 kg 3. 250 kg 4. 300 kgA 901000 kg spaceship has completed two thirds of its journey from the Earth to the Moon. At this position, what magnitude force would the ship's engines have to supply to be the equilibrant? Assume the mass of the moon is 7.35E+22 kg and the distance between the earth and the moon is 384000_km. 1. А. 3303_N 8536_N 7626_N 5080_N 5214 N F. D. В. Е. С. 9299.N
- Two manned satellites approaching one another at a relative speed of 0.150M/S intend to dock. The first has a mass of 3.00×10^3 kg, the second a mass of 7.50 x 10^3 kg . Assume that the positive direction is directed from the second satellite towards the first satellite. (a) Calculate the final velocity after docking, in the frame of reference in which the first set a lot was originally at rest. m/s ? (b) what is the loss of kinetic energy in this inelastic collision? j ? (c) repeat both parts in the frame of reference in which the second satellite was originally at rest. Final velocity m/s ? loss of kinetic energy j ? explain why the change in velocity is different in the two frames, where areas the change in kinetic energy is the same in both. I used ^ to show exponents7) Two manned satellites approaching one another, at a relative speed of 0.550 m/s, intending to dock. The first has a mass of 5.00 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. (a) Calculate the final velocity (after docking) in m/s by using the frame of reference in which the first satellite was originally at rest. (Assume the second satellite moves in the positive direction. Include the sign of the value in your answer.) _____m/s (b) What is the loss of kinetic energy (in J) in this inelastic collision? _____ J (c) Repeat both parts by using the frame of reference in which the second satellite was originally at rest. final velocity (m/s) _____ m/s loss of kinetic energy (J) _____ J Explain in detail why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.7) Two manned satellites approaching one another, at a relative speed of 0.550 m/s, intending to dock. The first has a mass of 5.00 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. (a) Calculate the final velocity (after docking) in m/s by using the frame of reference in which the first satellite was originally at rest. (Assume the second satellite moves in the positive direction. Include the sign of the value in your answer.) _____m/s (b) What is the loss of kinetic energy (in J) in this inelastic collision? _____ J (c) Repeat both parts by using the frame of reference in which the second satellite was originally at rest. final velocity (m/s) _____ m/s loss of kinetic energy (J) _____ J Explain in detail why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.
- Two manned satellites approaching one another at a relative speed of 0.300 m/s intend to dock. The first has a mass of 2.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. Assume that the positive direction is directed from the second satellite towards the first satellite. (a) Calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest.For what value of Q will the masses be held in place?Silid or to god o An object of mass m₁ = 4.00 kg is tied to an object of mass m2 = 4.00 kg with String 1 of length = 0.500 m. The combination is swung in a vertical circular path on a second string, String 2, of length = = 0.500 m. During the motion, the two strings are always collinear as shown in the figure. At the top of its motion, m2 is traveling at v = 4.80 m/s. Take the radial axis positive downward. (a) ( each mass. (b) What is the tension in String 1 at this instant? What is the tension in String 2 at (c) Draw the free body diagram of this instant? Which string will break first if the combination is rotated faster and faster? d) 1 m1 String 1 M DOVO dito 00101 String 2