Question

A truck of mass 10,000 kg climbs a vertical height of 200 m with the help of a 5000 N force. If its efficiency is 80%, calculate the additional mass that can be carried by the truck.

a) 10,000 kg
b) 7,500 kg
c) 15,000 kg
d) 5,000 kg

Answer 1

To calculate the additional mass that can be carried by the truck, we need to determine the work done by the truck and the work done by the 5000 N force. Using the work-energy principle and the truck's efficiency, we can solve for the additional mass.

Step-by-step explanation:

To calculate the additional mass that the truck can carry, we need to first determine the work done by the truck and the work done by the 5000 N force. The work done is equal to the force applied multiplied by the distance traveled, which is given as 200 m. The work done by the truck can be calculated using the efficiency of 80% as:

Work done by the truck = Efficiency x Work done by the force = 0.80 x (5000 N x 200 m)

Once we have the work done by the truck, we can use the work-energy principle to find the additional mass that can be carried. The work done by the truck is equal to the change in gravitational potential energy of the truck and the additional mass. We can set up the equation:

Work done by the truck = Change in gravitational potential energy of the truck + Change in gravitational potential energy of the additional mass

Solving for the additional mass:

Additional mass = (Work done by the truck - Change in gravitational potential energy of the truck) / g

Plugging in the values:

Additional mass = (0.80 x (5000 N x 200 m) - (10,000 kg x 9.8 m/s^2 x 200 m)) / 9.8 m/s^2

Calculating this equation gives us:

Additional mass ≈ 5,102.04 kg