We recently had a study group to look over some problems we were given in preparation for our upcoming exam. There were two problems that gave us a little bit of difficulty. There's a lot of stuff here, but I tried to trim it up as much as possible so as not to scare off any help. If I need to supply more information please let me know. Thanks in advance for any help/guidance provided.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

A NASA satellite has just observed an asteroid that is on a collision course with Earth. The asteroid has an estimated mass, based on its size, of5 x 109 kg. It is approaching the Earth on a head-on course with a velocity of600 m/srelative to the Earth and is now5 x 106 kmaway.

M_{asteroid}= 5 x 10^9 kg

M_{earth}= 5.98 x 10^24 kg

V_{i}= 600 m/s

r_{i}= 5 x 10^9 m

a. With what speed will it hit the Earth’s surface?

b. How much thermal energy will be released?

c. How much will the impact change the orbital velocity of the Earth?

2. Relevant equations

K_{i}+ U_{i}= K_{f}+ U_{f}

½M_{A}V_{i}² - G(M_{E}M_{A})/r_{i}= ½M_{A}V_{f}² - G(M_{E}M_{A})/r_{E}

½mv_{f}² - U_{g}= ½mv² - U_{g}

M_{A}V_{A}= (M_{A}+ M_{E})V

M_{A}V_{A}+ M_{E}V_{E}= (M_{A}+ M_{E})V_{f}

V_{f}= (M_{A}V_{A}) / (M_{A}+ M_{E})

3. The attempt at a solution

Part A we worked out using the first two equations in our study group:

½ (5 x 10^9 kg)(600 m/s)² - G(5.98x10^24 kg)( 5 x 10^9 kg)/(5 x 10^9 m)

and we ended up with1.12 x 10^4 m/srelative to Earth as our final answer.

Part B we were unsure how to work because we haven't covered anything in class regarding how much energy is released as thermal energy, light, and sound. Using the third and fourth equations from above we worked it out as such:

½(5 x 10^9 kg)(1.12 10^4 m/s)² - ½(5 x 10^9 kg)(5.017 x 10^-13)²

and ended up with a final answer of3.136 x 10^17 J.

Part C also left me with a certain level of uncertainty. Using the last two equations listed, I ended up with9.37 x 10^-12 m/sor3.14 x 10^15 %

1. The problem statement, all variables and given/known data

Two trees are7.6 mapart. Calculate the magnitude of the force F a backpacker must exert to hold a16 kgbackpack so that the rope sags at its midpoint by:

a. 1.5 m

b. 0.15 m

2. Relevant equations

Σt = (TsinΘ)(x) - mgh = 0

3. The attempt at a solution

For Part A we were confused as to what values we should use for x and h because the diagram shows the rope going across the trees to a pulley where the camper is applying the force to the rope. Some of us thought that we should use a distance of8.18 mfor x and4.09 mfor h based on the numbers we came up using trig. However, some argued that we should use distances of7.6 mand3.8 mbecause that is the distance between the trees. I maintained the opinion that the pulley would create more length in the rope, so I went with the first set of numbers I mentioned.

Θ = arctan(1.5/3.8) = 21.54º

Σt = Tsin(21.54º)(8.18 m) - (16 kg)(9.8 m/s²)(4.09 m) = 0

My final answer for part A was213.54 N

Part B offered no confusion because the distances obtained using trig were essentially7.6 mand3.8 m

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# Asteroid Collision Course and Sagging Backpack

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