Problem 1 A person stands on a bathroom scale inside an elevator that is at rest here on Earth where the acceleration due to gravity is approximately 9.8 m/s² straight down. The scale reads 650 N. The elevator suddenly begins to accelerate downward at a rate of 1.9 m/s². What does the scale read as the elevator accelerates? Don't forget units!
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- Concern the planet Mars, which has a radius of 3400 km. On Mars, the acceleration due to gravity is 3.72 m/s^2 The mass of the sun is 2.0×1030 kg, while the (actual) mass of Mars is 6.4×1023 kg. The average distance from Mars to the sun is 228 million kilometers. a. What is the gravitational force acting on Mars due to the sun? What is the reaction force to this force? Name or explain the force; don’t give a value. b. What are the speed and angular velocity of Mars? Compare the values to those of Earth. c. Using only information provided above, estimate the length of a year on Mars. Compare the value to that of Earth.I. A 10.0 kg mass is acted on by the two forces: F = (3.0N)î + (2.0N)j and F, = (10.0N)i + (-7.0N) a) Express the summation of these two forces in unit vector notation. That is: %3D %3! F=F F+F, b) What is the acceleration of this mass while these forces are acting? Write your answer in unit vector notation form. c) What is the direction of the acceleration (give the angle of acceleration with the x axis) and its magnetitude?A person of mass 50kg is falling at a terminal velocity of 60m/s. how much force does a superhero need to exert if it takes 0.1sec to stop the fall? If the person can withstand a maximum acceleration of 7g, what minimum time should it take the superhero to stop the fall? ans: 1.02s
- The height of a ball is thrown straight up sith a certain force is a function of the time (t) from which it is released given by f(t)=-0.5gt2+40t (where g is a constant determined by gravity). d. On the Earth g=32, but this value varies somewhat around the globe. If two locations had gravitational constants that differed by 0.1, what would be the difference in the maximum height of a ball tossed in the two places?Constants Every few hundred years most of the planets line up on the same side of the Sun. Part A Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line,(Figure 1). The masses are my — 0.815mE, тj — mean distances of the four planets from the Sun are 108, 150, 778, and 1430 million km. 318mв, mSat %3D 95.1mв, and the Figure 1 of 1 Express your answer to three significant figures and include the appropriate units.An object has a mass of 100 kg.a) How much does it weigh on Earth?b) How much does it weigh on the Moon (gmoon = 1.6 m/sz)?
- 1. Consider two vectors: A-10i +10j and B-5j+5k. a. Find the angle between A and B b. What is the magnitude and direction of C AXB? C. Suppose the position vector of an object M and N in an inertial frame is: Find the displacement vector of M relative to N, RMN, and the acceleration vector aMN of the object M relative to N, d. Calculate the angle Ø between Rmn and amn at time t-2.Assume that planet A has radius RA and mass MA, and planet B has radius Rg and mass Mg. Let ga and gB are the accelerations due to gravity at their surfaces, respectively. If MA = MB, and RA = 2Rg The ratio (g3/gA) is: А. 1 В. 2 С. 4 D. 0.5 E. 0.25 O A В O DImagine that you are an astronaut on a newly discovered planet. You discover information that gives you the planet’s mass and radius. How could you confirm that the gravitational constant G is the same there as on Earth? a. Drop an object from from a known height near the surface and time its fall to calculate g from 1/2at2, then use G = gr2/M to verify G. b. Drop an object near the surface and measure its falling time, calculate r from Earth’s g, then use G = gr2/M to verify G. c. Drop an object from orbit and time its fall to calculate g from 1/2at2, then use G = gr2/M to verify G. d. Drop an object from orbit and measure its falling time, calculate r from Earth’s g, then use G = gr2/M to verify G.
- Two forces act on a 2.90 kg object, the gravitational force and a second, constant force. The object starts from rest and in 1.20 s is displaced (4.10 3.30ĵ) m. Write the second force in unit vector notation. (Enter your answer in kg. m/s². Assume the gravitational force acts in the -ĵ direction.) kg. m/s² FAn object is shot straight upward from sea level with an initial velocity of 450 ft/sec. d.Assuming that gravity is the only force acting on the object, give an upper estimate for.its velocity after 5 sec have elapsed. Use g= 32 ft/sec for the gravitational acceleration. b.Using At= 1 sec, find a lower estimate for the height attained after 5 sec. %3D a. The upper estimate for the velocity after 5 sec is ft/sec. b. The lower estimate for the height after 5 sec is ft.Assume that planet A has radius RA and mass MA planet B has radius Rg and mass Mg. Let gA and g; are the accelerations due to gravity at their surfaces, respectively. If MA = Mg, and RA = 2Rg The ratio (ga/gB) is: and !! %3D А. 1 В. 2 C. 4 D. 0.5 E. 0.25