Question

The tops of the towers of the Golden Gate Bridge in San franciscoo , are 227 m above the water. Suppose a worker drops a 655 g wrench from the top of the tower. If the average force of air resistance is 0.141n , what will the kinetic energy of the wrench be when it hits the water

Answer 1

Kinetic energy is 1425.11 J.

Step-by-step explanation:

Given:

Mass of the wrench is,
`m=655\ g=0.655\ kg`

Height of fall is,
`h=227\ m`

Force of resistance is,
`F=0.141\ N`

Now, the total energy at the top is equal to the potential energy of the wrench at the top since the kinetic energy at the top is 0.

Now, potential energy at the top is given as:

`U=mgh\\U=0.655* 9.8* 227\\U=1457.113\ J`

Now, the potential energy at the top is converted to kinetic energy at the bottom and some energy is wasted in overcoming the resistance force by air.

Potential Energy = Kinetic energy + Energy to overcome resistance.

⇒ Kinetic energy = Potential Energy - Energy to overcome resistance.

Energy to overcome resistance force is the work done by the wrench against the resistance force and is given as:

`W_(res)=Fh=0.141* 227=32.007\ J`

Therefore, Kinetic energy at the bottom is given as:

`K=U-W_(res)\\\\K=1457.113\ J - 32.007\ J\\\\K=1425.106\approx1425.11\ J`

Hence, the kinetic energy of the wrench be when it hits the water is 1425.11 J.