Ask Question
4 November, 04:41

You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface. Sofia, with mass 80.0 kg, is given a push and slides eastward. Elena, with mass 55.0 kg, is sent sliding northward. They collide, and after the collision, Sofia is moving at 39.0 ∘ north of east with a speed of 6.40 m/sm/s and Elena is moving at 20.0 ∘ south of east with a speed of 9.40 m/s.

a. What was the speed of each person before the collision?

b. By how much did the total kinetic energy of the two people decrease during the collision?

+3
Answers (1)
  1. 4 November, 07:19
    0
    a) V_ei = 2.6434 m/s, V_si = 11.05 m/s

    b) Loss K. E = 1007.958 J

    Explanation:

    Given:

    - Mass of Sofia Ms = 80 kg

    - Mass of Elena Me = 55 kg

    - The initial velocity of Sofia = V_si

    - The initial velocity of Elena = V_ei

    - The final velocity of Sofia V_sf = 6.4 m/s

    - The final velocity of Elena V_ef = 9.4 m/s

    - The angle sophia makes with east direction towards north θ_1 = 39°

    - The angle Elena makes with east direction towards south θ_2 = - 20°

    Find:

    a. What was the speed of each person before the collision?

    b. By how much did the total kinetic energy of the two people decrease during the collision?

    Solution:

    - Since no eternal forces are acting on either Sophia or Elena, then the momentum of both is conserved in all directions.

    - Using conservation of momentum in north-south direction. Taking north as positive and south as negative:

    Me*V_ei = Me*V_ef*sin (θ_2) + Ms*V_sf*sin (θ_1)

    Plug values in:

    55*V_ei = 55 * (9.4) * sin (-20) + 80*6.4*sin (39)

    55*V_ei = 145.38762

    V_ei = 2.6434 m/s

    - Using conservation of momentum in east-west direction. Taking east as positive and west as negative:

    Ms*V_si = Me*V_ef*cos (θ_2) + Ms*V_sf*cos (θ_1)

    Plug values in:

    80*V_si = 55 * (9.4) * cos (-20) + 80*6.4*cos (39)

    80*V_si = 883.71981

    V_si = 11.05 m/s

    - The total kinetic energy of both elena and sophia before collision is given by:

    K. E_i = 0.5*Me*V_ei^2 + 0.5*Ms*V_si^2

    K. E_i = 0.5*55*2.6434^2 + 0.5*80*11.05^2

    K. E_i = 5076.258 J

    - The total kinetic energy of both elena and sophia after collision is given by:

    K. E_f = 0.5*Me*V_ef^2 + 0.5*Ms*V_sf^2

    K. E_f = 0.5*55*9.4^2 + 0.5*80*6.4^2

    K. E_f = 4068.3 J

    - The loss in kinetic energy after collision is given by:

    Loss K. E = K. E_i - K. E_f

    Loss K. E = 5076.258 - 4068.3

    Loss K. E = 1007.958 J
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface. Sofia, with mass ...” in 📙 Physics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers