Question

A small sphere of mass m = 7.50 g and charge q 1 = 32.0 nC is attached to the end of a string and hangs vertically as in Figure P15.4. A second charge of equal mass and charge q 2 = 258.0 nC is located below the first charge a distance d = 2.00 cm below the first charge as in Figure P15.4. (a) Find the tension in the string. (b) If the string can withstand a maximum tension of 0.180 N, what is the smallest value d can have before the string breaks

Accepted Answer

(a)
Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges. 11eb7e53_1a4f_4595_bc75_85fa73214cfa_SM7473_11 Here, 11eb7e53_1a4f_4596_bc75_c5f64137b7f8_SM7473_11 is the Coulomb's constant, 11eb7e53_1a4f_4597_bc75_b5096ae679e8_SM7473_11 is the charge of the particle 1, 11eb7e53_1a4f_4598_bc75_918925723b35_SM7473_11 is the charge of the particle 2, and 11eb7e53_1a4f_4599_bc75_25e1029ec623_SM7473_11 is the distance between the two particles.
Substitute 11eb7e53_1a4f_459a_bc75_adde9a1cb6d8_SM7473_11 for 11eb7e53_1a4f_459b_bc75_d58af432dc04_SM7473_11 , 11eb7e53_1a4f_459c_bc75_0750d025f09c_SM7473_11 for 11eb7e53_1a4f_459d_bc75_1b3fe10648d8_SM7473_11 , 11eb7e53_1a4f_459e_bc75_6da6619e33bd_SM7473_11 for 11eb7e53_1a4f_6caf_bc75_9bb58cd7d415_SM7473_11 , and 11eb7e53_1a4f_93c0_bc75_f196e700a8ba_SM7473_11 for 11eb7e53_1a4f_93c1_bc75_91703617b942_SM7473_11 . 11eb7e53_1a4f_93c2_bc75_47f775ea7259_SM7473_00 The tension T in the string is pointed in an upward direction and the gravitational force 11eb7e53_1a4f_93c3_bc75_933ff4cb5ba1_SM7473_11 is pointed in a downward direction. The electrical Coulomb force 11eb7e53_1a4f_93c4_bc75_8d804d5597f5_SM7473_11 exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium. 11eb7e53_1a4f_93c5_bc75_eb5d990a492f_SM7473_11 Here, 11eb7e53_1a4f_93c6_bc75_6bb557564311_SM7473_11 is the mass of each particle and 11eb7e53_1a4f_93c7_bc75_e323c9ad3e1f_SM7473_11 is the acceleration due to gravity.
Rewrite the equation for 11eb7e53_1a4f_93c8_bc75_699db93eff1c_SM7473_11 . 11eb7e53_1a4f_93c9_bc75_270cd859f25e_SM7473_11 Substitute 11eb7e53_1a4f_93ca_bc75_cb4e9a7c0632_SM7473_11 for 11eb7e53_1a4f_93cb_bc75_213597b86033_SM7473_11 , 11eb7e53_1a4f_93cc_bc75_d31960238e1e_SM7473_11 for 11eb7e53_1a4f_93cd_bc75_51ca7372d658_SM7473_11 , and 11eb7e53_1a4f_93ce_bc75_9b733d288855_SM7473_11 for 11eb7e53_1a4f_93cf_bc75_454ec34c21a8_SM7473_11 . 11eb7e53_1a4f_93d0_bc75_71f673d6891c_SM7473_11 Therefore, the tension in the string is 11eb7e53_1a4f_93d1_bc75_2f6d0896383e_SM7473_11 . 
(b)
Let 11eb7e53_1a4f_bae2_bc75_cba311fe6d38_SM7473_11 be the new distance between the two charges and 11eb7e53_1a4f_bae3_bc75_77d362c6e3f0_SM7473_11 be the maximum tension in the string. Thus, the net force exerted on the system is, 11eb7e53_1a4f_bae4_bc75_5dbae983bace_SM7473_11 Rewrite the equation for 11eb7e53_1a4f_bae5_bc75_a5360c68eef6_SM7473_11 . 11eb7e53_1a4f_bae6_bc75_37864adf097e_SM7473_11 Substitute 11eb7e53_1a4f_e1f7_bc75_d5d80c204166_SM7473_11 for 11eb7e53_1a4f_e1f8_bc75_8501a647fd1b_SM7473_11 , 11eb7e53_1a4f_e1f9_bc75_7b0213cfd75d_SM7473_11 for 11eb7e53_1a4f_e1fa_bc75_b700f8ef52b2_SM7473_11 , 11eb7e53_1a4f_e1fb_bc75_31782415107c_SM7473_11 for 11eb7e53_1a4f_e1fc_bc75_894d7cda4302_SM7473_11 , 11eb7e53_1a50_090d_bc75_171b95bd2624_SM7473_11 for 11eb7e53_1a50_090e_bc75_b181b0bc86c1_SM7473_11 , 11eb7e53_1a50_090f_bc75_ad7fcd7bda2a_SM7473_11 for 11eb7e53_1a50_5630_bc75_1fe221216eda_SM7473_11 , and 11eb7e53_1a50_5631_bc75_17bb1959cf0f_SM7473_11 for 11eb7e53_1a50_5632_bc75_a5e2c8fd79e2_SM7473_11 . 11eb7e53_1a50_5633_bc75_65aa8c0da0b4_SM7473_00 Therefore, the smallest value of distance d possible before the string breaks is 11eb7e53_1a50_5634_bc75_f7713d7739d0_SM7473_11 .

College Physics 10th Edition by Raymond Serway,Chris Vuille

College Physics 10th Edition by Raymond Serway,Chris Vuille