Question

16. A 7500 kg 18-wheeler traveling at 20 m/s exits onto the runaway truck ramp on the freeway.

When it comes to a stop, it is 10 m higher than before.
How much energy was dissipated by friction?

Answer 1

765,000 Joule

Step-by-step explanation:

Principle of Conservation of Energy

The total energy in an isolated system cannot be created or destroyed, but transformed. Moving objects have kinetic energy, objects placed in some height above a reference level have gravitational potential energy. When they change their motion variables, one energy converts into the other, but if the numbers don't fit, we know there was some other type of energy acting into the system. The most common reason for energy 'losses' is the thermal energy, produced when objects move in rough surfaces or take friction from the air.

The 7,500 kg truck is originally traveling at 20 m/s to a certain height we'll set to 0. Thus, its total energy is

`\displaystyle E_1=(mv^2)/(2)`

`\displaystyle E_1=(7,500\ 20^2)/(2)`

`E_1=1,500,000\ Joule`

When it comes to a stop, its speed is 0 and its height is 10 m higher than before. It means all the kinetic energy was transformed into other types of energy. The gravitational potential energy is

`U=mgh=(7,500)(9.8)(10)=735,000\ Joule`

Since this number is not equal to the previous value of the energy, the difference is due to thermal energy dissipated by friction

`E_t=1,500,000\ Joule-735,000\ Joule=765,000\ Joule`