Consider a satellite of mass mị that orbits a planet of mass m2 in a circle a distance r from the center of the planet. The satellite's mass is negligible compared with that of the planet. Indicate whether each of the statements in this problem is true or false. The information given is sufficient to uniquely specify the speed, potential energy, and angular momentum of the satellite. O true O false Part B The total mechanical energy of the satellite is conserved. O true O false Part C The linear momentum vector of the satellite is conserved. O true

A 1.15 kg mass is attached to a 1.86 m string that is anchored to the ceiling. The mass is pulled back to an initial angle of theta = 65.1 degrees and released from rest. (a) How fast is the ball moving at the bottom of its swing — the position indicated in the figure? (b) What is the tension in the string at the bottom of the swing — the position indicated in the figure?

R R A mass m = 88 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 15.8 m and finally a flat straight section at the same height as the center of the loop (15.8 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.) 1) What is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? m/s Submit 2) What height above the ground must the mass begin to make it around the loop-the-loop? m Submit 3) If the mass has just enough speed to make around the loop without leaving the track, what will its speed be at the bottom of the loop? m/s Submit +

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Four identical masses of 7.3 grams are placed at the corners of a square with a side length of d = 27 cm, as shown below. What is the gravitational potential energy of the system? d d

Plan A - Get people off the Earth in a permanent space habitat. Recall that the gravitational potential energy of an object in orbit around the Earth has magnitude GMmd where M is the mass of the Earth and m is the mass of the object in orbit around it (G = 6.67×10-11Nm2/kg2).  If this is also equal to the energy that must be expended (work) to place the object at orbital altitude d, i. calculate the work required to place 100 million people in orbit at 300 miles altitude. Use a mass of 70 kg for the average mass per person.  (1 Joule=1 Nm) ii. How does this compare to the current annual energy consumption of the United States? (1 Watt hour = 3600 Joules)

A satellite has a mass of 298 kg and is located at 1.97 ✕ 106 m above the surface of Earth. (a) What is the potential energy associated with the satellite at this location? J(b) What is the magnitude of the gravitational force on the satellite? N

A force in the +z-direction with magnitude 18.0 N- (0.530 N/m)z is applied to a 6.60 kg box F(x) that is sitting on the horizontal, frictionless surface of a frozen lake. F(x) is the only horizontal force on the box. O Part A If the box is initially at rest at r = 0, what is its speed after it has traveled 16.0 m ? Express your answer to three significant figures and include the appropriate units. ? HA Value Units Submit Previous Answers Request Answer

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. Each step is of uniform height d. The mass of each object is a multiple of the base mass m: object 1 has mass 4.60m, object 2 has mass 2.21m, and object 3 has mass m. When the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. If the objects are then relocated as shown, what is the new total potential energy of the system? Each answer requires the numerical coefficient to an algebraic expression. Each algebraic expression is given using some combination of the variables m, g, and d, where g is the acceleration due to gravity. Enter only the numerical coefficient. (Example: If the answer is 1.23mgd, just enter 1.23) This potential energy was calculated relative to the bottom of the stairs. If you were to redefine the reference height such that the total potential energy of the system became zero, how high…

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