Question

a semi truck has a mass of 1000kg and is traveling at a constant velocity of 3m/s. suddenly, the driver sees a herd of cows on the road ahead and locks his brakes, causing the truck to skid. if all the tires combined can only do a maximum of 5,000j worth of work before they burn up. will the truck be able to stop without blowing its tires?
yes, since the total kinetic energy which the tires will need to transfer out of the system is less than 5,000j.
yes, since the tires do not have to do any work because the kinetic energy of the truck will be turned into potential energy by the brakes.
no, since the truck had to stop suddenly, the momentum of its change in kinetic energy would blow the tires.
no, since the total kinetic energy which the tires will need to transfer out of the system is greater than 5,000j.

Explanation:

Step1: Calculate Kinetic Energy

The formula for kinetic energy (KE) is $KE = \frac{1}{2}mv^2$, where $m = 1000\,\text{kg}$ and $v = 3\,\text{m/s}$.
Substitute values: $KE = \frac{1}{2} \times 1000 \times 3^2 = 500 \times 9 = 4500\,\text{J}$.

Step2: Compare KE with Work Capacity

The tires can do a maximum of $5000\,\text{J}$ of work. Since $4500\,\text{J} < 5000\,\text{J}$, the kinetic energy to transfer is less than the tires’ work capacity.

Answer:

Yes, since the total kinetic energy which the tires will need to transfer out of the system is less than 5,000J.