Suppose iI want to buy a cable that will support & pull a mass of 2kg$2\ kg$ upward at an acceleration rate of 2 meter/secound$^2$ i$2 m/s^2$, I must specify the maximum mass the cable will carry:.
iI know how to calculate the tension in the cable :
thereThere are 2 forces acting on the mass:
1)the force of the cable pulling up which is unknown, call it "Ft"
2)the force of the gravity of the earth pulling down call it "Fw"
The force of the cable pulling up which is unknown, call it "$F_t$"
The force of the gravity of the earth pulling down call it "$F_w$"
since the mass is moving upward at an acceleration rate of 2m/s$^2$$2m/s^2$, then the resultant force affecting on the mass $\underline{ΣF}$$ΣF$ must be F=2kg$\times$2m/s$^2$=4Newton$F=2kg\times 2m/s^2=4N$
$$ΣF = Ft\; -Fw$$$$ΣF = F_t\; -F_w$$ Add +Fw$+F_w$ to both sides: $$Ft = Fw+ΣF$$$$F_t = F_w+ΣF$$ $$Ft = mg + ma$$$$F_t = mg + ma$$ $$Ft = 2\times9.81 + 2\times2 =23.62N$$$$F_t = 2\times9.81 + 2\times2 =23.62N$$
nowNow how can iI express this force in kilogram should iI divide it by 9.81m/s$^2$$9.81m/s^2$ which is acceleration due to gravity or divide it by 2m/s$^2$$2m/s^2$
iI can express the same problem horizontally:
a 2kg trailer is pulled to the right on a frictionless surface by a cable connected to a train moving at an acceleration rate of 0.5m/s$^2$ , what is weight on the cable during acceleration of the trailer?
A $2kg$ trailer is pulled to the right on a frictionless surface by a cable connected to a train moving at an acceleration rate of $0.5m/s^2$ , what is weight on the cable during acceleration of the trailer?
iI know that the tension on the cable is F=ma=2$\times$0$F=ma=2\times0.5=1N$ .5=1N but But again if iI want to buy that cable iI must specify the maximum mass the cable will carry, is it correct to say that this mass = (1/9.81)=0.102kg$= (1/9.81)=0.102kg$ ?
