UNIT 4
PHYS 2001
Example 01
Example 02
Example 03
Example 04
Example 05
Example 06
Example 07

 

 

Gravitation - Example 05

 

Projectiles

Fig 5

5. In Fig. 5, three 5.00 kg spheres are located at distances d1 = 0.300 m and d2 = 0.400 m.
(a) What is the magnitude of the net gravitational force on sphere B due to spheres A and C? 
(b) What is the direction (relative to the positive direction of the x axis) of the net gravitational force on sphere B due to spheres A and C?
(c)  What linear speed must an Earth satellite have to be in a circular orbit at an altitude of 160 km above Earth’s surface?
(d) What is the period of revolution?

Information given:
Mass of A = 5.00kg
Mass of B = 5.00kg
Mass of C = 5.00kg

We know G = 6.67 x 10-11 Nm2kg-2.

(a) Using F = GmM/r2,
FBA = [6.67 x 10-11 Nm2kg2 (5kg) (5kg)] / (0.300 m)2
FBA = 1.85 × 10−8 N

FBC = [6.67 x 10-11 Nm2kg2 (5kg) (5kg)] / (0.400 m)2
FBC =1.04 × 10−8 N

we find that the A pulls upward on B with 1.85 × 10-8 N, and C pulls to the righton B with 1.04 × 10−8 N
Thus, the net force canbe found by using Pythagoras:

(FN)2 = (1.85 × 10−8 N)2 + (1.04 × 10−8 N)2

(FN) = (2.13 × 10−8 N

(b) Tan θ = (1.85 × 10−8 N) / (1.04 × 10−8 N)

θ = 60.7° to the line BC

(c) Information given:

Altitude of satellite = 160 km = 1.60 x 105 m

We know G = 6.67 x 10-11 Nm2kg-2.

We know Mass of the Earth = 5.98 x 1024 kg

We know Radius of the Earth = 6.37 x 106 m

radius of orbit r = Altitude of satellite + Radius of the Earth

r = 1.60 x 105 m + 6.37 x 106 m

r = 6.53 x 106 m

The centripetal acceleration is given by Fc = mv2/r and is provided by the gravitation force F = GmM/r where r is the radius of orbit and M is the mass of the earth and m is the mass of the satellite

So mv2/r = GmM/r2

v2 = GM/r

v2 = (6.67 x 10-11 Nm2kg-2) ( 5.98 x 1024 kg) / (6.53 x 106 m)

v = 7.82 x 103 ms-1

(d) T = 2πr/v

T = 2π(6.53 x 106 m) / (7.82 x 103 ms-1)

T = 5.23 x 10s s

T =

87.4 minutes
 

 

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Concept by Kishore Lal. Programmed by Kishore Lal... Copyright © 2015 Kishore Lal. All rights reserved.