Question

A tow truck is using a cable to pull a car up a 15 degree hill. If the car weighs 4000 lbs and the cable has a diameter of .75 inches, find the stress in the cable when the truck comes to a stop while on the hill. Ignore friction between the car and the pavement.

Answer 1

Answer:40.603 MPa

Step-by-step explanation:

Given

Car weighs (m)4000 lbs
`\approx 1814.37 kg`

diameter of cable(d)
`=0.75 in.\approx 19.05 mm`

Hill angle
`\theta =15^(\circ)`

Now

tension in cable will bear the weight of car acting parallel to rope which is
`mgsin\theta`

Thus

`T=mgsin\theta`

`T=1814.37* 9.81* sin(15)=11,574.45 N`

T=11.57 kN

thus stress(
`\sigma`)=
`(T)/(A)`

where A=cross section of wire
`=285.059 mm^2`

`\sigma =(11574.45)/(285.059)=40.603 MPa`