Final answer:
To determine the additional mass the truck cab carry, we need to calculate the work done by the truck and then divide it by the work done per unit mass. The additional mass the truck can bear is approximately 51 kg.
Step-by-step explanation:
To determine the additional mass the truck can carry, we need to calculate the work done by the truck and then divide it by the work done per unit mass. The work done by the truck is given by the product of the force and the distance traveled, which is 5000 N * 20 km = 100,000 J. The work done per unit mass is equal to the gravitational potential energy gained per unit mass, which is the change in gravitational potential energy divided by the mass of the truck. We can use the formula for gravitational potential energy, mgh, where m is the mass, g is the acceleration due to gravity, and h is the height climbed. Substituting the given values, we get (10,000 kg)(9.8 m/s^2)(200 m) = 1.96 x 10^7 J. The work done per unit mass is then (1.96 x 10^7 J)/(10,000 kg) = 1960 J/kg. To find the additional mass the truck can carry, we divide the work done by the work done per unit mass, which is 100,000 J / 1960 J/kg = 51.02 kg. Therefore, the additional mass the truck can bear is approximately 51 kg.