In deep space, sphere Aof mass 20kgis located at the origin of an x-axis and sphere Bof mass10kg is located on the axis atx=0.80m . Sphere Bis released from rest while sphere Ais held at the origin. (a) What is the gravitational potential energy of the two-sphere system just as Bis released? (b) What is the kinetic energy of Bwhen it has moved 0.20mtoward A?

Short Answer

Expert verified

a. The gravitational potential energy of the two-sphere system just as B is released is-1.7×10-8J

b. The kinetic energy of B when it has moved 0.20mtowards A is 5.6×10-9J.

Step by step solution

01

Step 1: Given

Sphere A,MA=20kgat originx=0mand

Sphere B, MB=10kg at x=0.80m

02

Determining the concept

Using the formula of gravitational potential energy and the principle of conservation of energy, find thegravitational potential energy of the two-sphere system just as B is released and the kinetic energy of B when it has moved towards Arespectively. According to the law ofconservation of energy, energy can neither be created nor be destroyed.

Formulae are as follows:

Ui+Ki=Uf+KfU=GMAMBRK=12mv2

where, MA,MB, m are masses, R is the radius, v is velocity, G is gravitational constant, K is kinetic energy and U is potential energy.

03

(a) Determining the gravitational potential energy of the two-sphere system just as   is released

Now,

Ui=-GMAMBri

As

MA=20kg,MB=10kg,andri=0.80mUi=-6.67×10- 11m3s2·kg20kg10kg0.80m=-1.7×10-8J

Hence, the gravitational potential energy of the two-sphere system just as B is released is -1.7×10-8J.

04

(b) Determining the kinetic energy of  B when it has moved  0.20m towards  A

Now,

Ui+Ki=Uf+Kf

As

Ui=-1.7×10-8J,andKi=0ri=0.80m-0.20m=0.60m

-1.7×10-8J=K-6.67×10- 11m3s2·kg20kg10kg0.60m-1.7×10-8J=K-2.22×10-8JK=5.6×10-9J

Hence, the kinetic energy of when it has moved 0.20mtowards A is 5.6×10-9J.

Therefore, using the formula for gravitational potential energy and the law of conservation of energy, kinetic energy can be found.

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