Ropes 3 m and 5 m in length are fastened to a holiday decoration that is suspended over a town square. the decoration has a mass of 10 kg. the ropes, fastened at different heights, make angles of 52° and 40° with the horizontal. find the tension in each wire and the magnitude of each tension. (use g = 9.8 m/s2 for the acceleration due to gravity. round your answers to two decimal places.)

T₁= 75.25 N : Wire tension forming angle of 52° with horizontal

T₂ = 60.49 N : Wire tension forming angle of 40° with horizontal

Explanation:

We apply Newton's first law to the holiday decoration in equilibrium

Forces acting on holiday decoration:

T₁ : Wire tension forming angle of 52° with horizontal

T₂ : Wire tension forming angle of 40° with horizontal

W= m*g=  10 kg*9.8 m/s² = 98 N : weight of the decoration

∑Fx=0

T₁x -T₂x = 0

T₁x = T₂x

T₁*cos52° = T₂*cos40°

T₁= T₂*(cos40°) / (cos52°)

T₁= 1.244T₂ Equation (1)

∑Fy=0

T₁y+T₂y -W = 0

T₁*sin52° + T₂*sin40° - 98 = 0 Equation (2)

We replace T₁ of the equation (1) in the equation (2)

1.244T₂*sin52° + T₂*sin40° - 98 = 0

0.98T₂ + 0.643T₂ = 98

1.62T₂ = 98

T₂ = 98 / 1.62

T₂ = 60.49 N

We replace T₂ = 60.49 N in the Equation (1)

T₁= 1.244*60.49 N

T₁= 75.25 N

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.

1= 26.17

2= 1.17

3=30.86

4=5.86

just took the assigment on edge