Ask Experts Questions for FREE Help !
Ask
    western50's Avatar
    western50 Posts: 105, Reputation: 1
    Junior Member
     
    #1

    Nov 6, 2010, 10:08 PM
    gravitatioinal force and springs (i am not sure about what i got)
    Planet X of mass m1 orbits a Sun in uniform circular motion at a distance r1 and speed v1. The mass of the Sun is MS1 and its radius is RS1 as shown in the figure below.



    1. If the planet's mass were doubled, how would a, the magnitude of its acceleration, change?

    a would decrease.
    a would remain the same.
    a would increase.

    Consider another solar system in which Planet Y of mass m2 = 2 m1 orbits a Sun of mass MS2 = 2 MS1 and radius RS2 = 2RS1 at a distance r2 = 2r1. Further, suppose R2, the radius of Planet Y is twice R1, the radius of Planet X.

    2. How would w2, your weight on Planet Y, compare to w1, your weight on Planet X?

    w2 < w1
    w2 = w1
    w2 > w1

    3. How does P2, the period of the orbit of the Planet Y, compare to P1, the period of the orbit of Planet X

    P2 = (1/2) P1
    P2 = P1
    P2 = 2 P1
    P2 = 4 P1
    We do not have enough information to answer this question. We need to be given v2, the speed of the second planet in its orbit.



    A block of mass M rests on a frictionless inclined plane of angle θ as shown in the diagram below. Two springs of equal length are connected to the block and to two posts as shown. The separation between the posts is equal to the sum of relaxed lengths of the springs and the length of the block.



    4. The force the bottom spring exerts on the block is in the opposite direction of the force that the top spring exerts on the block.

    TRUE
    FALSE

    5. Suppose the top (bottom) spring is stretched (compressed) from its relaxed length by an amount δx = 0.082 m. If the spring constant of the top spring is twice that of the bottom spring and M = 0.25 kg and θ = 30o, what is k, the spring constant of the bottom spring?

    k = 1.66 N/m
    k = 2.22 N/m
    k = 3.33 N/m
    k = 4.98 N/m
    k = 6.44 N/m
    western50's Avatar
    western50 Posts: 105, Reputation: 1
    Junior Member
     
    #2

    Nov 6, 2010, 10:26 PM
    here is what I thought, but I am not sure

    1. a would be the same because the mass of the planet would not be matter, it is only the mass of the center being orbited matter.
    2. weight 2 is smaller than weight 1 because gravity on planet X to the gravity of planet Y is 2, and mass remains constant, so weight 2 is also smaller than weight 1
    3. my concern is "will velocity of a planet be different if the orbital radius is different"?
    4. I think both forces are at the same direction by looking at the restoring force
    5. I drew a free body diagram for the block, and it is F(spring bottom)+F(spring up)-Mgsin(angle)=0, is this the right equation? So the answer would be 4.98?
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
     
    #3

    Nov 7, 2010, 10:47 AM

    1. Right.

    But it's actually because:





    m cancels, so, the acceleration depends on M, r and v. (M

    2. Right.

    3. I'll use another equation for this part just so not make use of everything we have.





    For planet 2:





    So,







    4. Right.

    5. Right!

    Well done :)
    western50's Avatar
    western50 Posts: 105, Reputation: 1
    Junior Member
     
    #4

    Nov 7, 2010, 07:52 PM
    What is T1 and T2, and how does that related to weight 1 and weight 2?
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
     
    #5

    Nov 7, 2010, 10:04 PM

    T1 and T2 are the periodic Times of planet 1 and planet 2. I just like to use the same notation where I use them. In the context of the question, T1 is the same as P1 and T2 that same as P2. :)
    western50's Avatar
    western50 Posts: 105, Reputation: 1
    Junior Member
     
    #6

    Nov 9, 2010, 09:48 PM
    I still don't get question three because isn't it the speed of planet Y is not given, then how can you find out the relationship?
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
     
    #7

    Nov 9, 2010, 09:56 PM

    I just showed you that you don't need it's speed.

    What is important, is that you have the force which provides the centripetal force, which is gravity.

    Once you have that force, there is only one speed that the planet can have to remain in circular motion.

    For this question, I didn't make use of the linear speed of the planet, but it's angular speed. (denoted by omega) which is directly related to the periodic time.
    harum's Avatar
    harum Posts: 339, Reputation: 27
    Full Member
     
    #8

    Nov 9, 2010, 10:17 PM

    Look back at how you solved Q1 and remember that for circular motion, if you know acceleration and radius, then you know the speed.
    jkwoner's Avatar
    jkwoner Posts: 1, Reputation: 1
    New Member
     
    #9

    Nov 10, 2010, 08:18 PM
    For question 4, is it true or false?
    I think it's true because the restoring force of the bottom spring pulls box down
    While the restoring force of the top spring pulls box up...

    Am I correct?
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
     
    #10

    Nov 10, 2010, 11:32 PM

    That's what western50 said and I agreed :)

Not your question? Ask your question View similar questions

 

Question Tools Search this Question
Search this Question:

Advanced Search

Add your answer here.


Check out some similar questions!

How can a force transferred person force a more senior employee to go to a different [ 1 Answers ]

2 employees with less seniority have been put in my department and now I have been forced to a different shift

Can the force of an elastic band be equated to a certain poundage of force? [ 2 Answers ]

This seems like a simple yes, but here is my confusion. A band snaps back faster than an object would free fall. So even if a stretched band was 20 pounds of force, it is pulling at a higher velocity than a twenty pound weight. For example if you do an arm curl with a 20 pounds weight, it...

Find force of gravity, normal force, and net force in Physics [ 6 Answers ]

A crate of mass m (=10 kg) is placed at rest on a (frictionless) inclined plane, which has an angle (= 30 deg ) above horizontal 1. The force of gravity on the crate is? 2. The normal force on the crate is? 3. The net force on the crate is? 4. How long would it take the crate to slide 8 m...

At what value of Force, can we feel the effect of gravitational force between objects [ 2 Answers ]

PLEASE READ THE WHOLE QUESTION AND THEN ANSWER At what value of Force, could we feel or see the effect of gravitational pull or force between two objects. E.g. 2 pencils kept at a very small distance (r) exert a force (F) on each other such that they are pulled by each other and stick to each...

Compression springs and extension springs [ 2 Answers ]

I am an artist trying to figure out which extension spring to buy to hold back three compression springs. I am using 3 compression springs with the following attributes: deflection a load = 1.1" load lbs =1.95 and rate lbs/in = 1.77 (these are the specs in the catalog) they are stacked in a...


View more questions Search