course Phy 241
61) The space shuttle Endeavour with mass 86,400kg, is in a circular orbit of radius 6.66 x 10^6 m around the Earth. It takes 90.1 minutes for the shuttle to complete each orbit. On a repair mission, it is cautiously moving 1.00m closer to a disabled satellite every 3.00 s. Calculate the shuttle’s kinetic energy a) relative to the Earth b)relative to the satellite.
To find the KE relative to the satellite you can use KE=.5mv^2 =.5(86400)(1.00/3.00)^2=4800J .
To find the KE from Earth we first have to convert the 90.1 to minutes, but I am not sure how to work with the circular orbit.
Find the circumference, and divide that by the time required to complete the orbit.
64)An object is attracted toward the origin with a force given by Fx=-k/x^2. (Gravitational and electrical forces have this distance dependence.) a) calculate the work done by the force Fx when the object moves in the x direction from x1 to x2. If x2>x1, is the work done by Fx positive or negative? B) The only other force acting on the object is a force that you exert with your hand to move the object slowly from x1 to x2. How much do you do? If x2>x1, is the work you do positive or negative? C) explain the similarities and differences between your answers to parts a and b.
a)W is defined by F`ds so W=-k/x^2 (x2-x1). Since k is negative and the `ds will be positive W should be negative for this case.
The force is variable. There is no single force on the interval, because x varies over the interval.
Can you set up a Riemann sum to represent the approximate work?
Start by finding the work done over a small interval of unspecified width `dx, and let x_rep be a representative value of x within the interval (since the interval is small, the representative point can be anywhere in the interval, so x_rep can be any x within the interval).
Then assume a series of small intervals `dx_1, `dx_2, ..., `dx_n with representative points x_rep_1, x_rep_2, ..., x_rep_n. Write the expression for `dW_i, where i is any number between 1 and n.
Then write the expression for sum(`dW_i), where the summation is assumed to go from i = 1 to n. Assuming that the intervals `dx_1, ..., `dx_n represent a partition of the interval from x = x1 to x = x2 (a partition is a subdivision of an interval into distinct subintervals), this expression will represent the total work done between x1 and x2.
If the 'mesh' of the partition then approaches 0 (the 'mesh' is the size of the largest of the subintervals), then n will approach infinity, and the sum will approach an integral. What is this integral?
Get back to me with the best answers you can provide to these questions, and of course with additional questions if they arise.
If you are moving the object in the same direction as the magnetic force, then you should also be doing negative work, but I am not sure how to calculate how a much.
69) A small block with a mass of .12 kg is attached to a cord passing through a hole in a frictionless, horizontal surface. The block is originally revolving at a distance of .4 m from the hole with a speed of .7 m/s. The cord is then pulled form below, shorteneing the radius of the circle in which the block revolves to .1 m. At this new distance, the speed of the block is observed to be 2.8 m/s.
a) What is the Tension in the cord in the original situation when the blovck has speed v= .7 m/s?
b) What is the tension in the cord in the final situation when the block has speed v = 2.8 m/s?
c) How much work was done by the person who pulled on the cord?
To find Tension we can use the equation T-mg=ma. First we need to find a. I am not sure how to find a. I know we can use vf^2=v0^2+2a`ds, but I am not sure if V0 can be assumed to be 0 because I tried this and did not get the answer in the back of the book.
The net force on an object moving in a circular path is the centripetal force a = v^2 / r, directed toward the center of the circle. This is where you start.
To answer the last question use the work-energy theorem.
72) A net force with magnitude (5.00N/m^2)x^2 and directed at a constant angle of 31 degrees with the positive x axis acts on an object of mass .25 kg as the object moves parallel to the x axis. How fast is the object moving at x = 1.5 mif it has a speed of 4 m/s at x=1m? We know that F=ma and if the net force is 5.00x^2 we can use a={5.00x^2(cos31)}/.25, then we can use KE=F`ds, so that .5(.25)v^2=.25(17.14*1.5^2)(.5). Solving for v we get 6.21 m/s.
You have the right idea, but KE is not equal to F `ds. It is so that
`dKE = F_net `ds.
But `dKE is the change in KE, equal to KE_f - KE_0, the difference between initial and final KE.
Can you modify your solution accordingly?