Question

A toy car with a mass of 1 kg starts from rest at the top of a ramp at point A. The toy car is released from rest, rolls 2 meters down the ramp, then another 3 meters across the floor to point B where its speed is measured to be 4.24 m/s. The air exerts a resistance force of 2.0 N on the car as it moves from A to B. Find the initial height of the car at point A. Assume g = 10 m/s^2. Note: The user has mastered the concept of the conservation of energy and is proficient in solving problems where energy is conserved but is new to solving energy problems involving work done by non-conservative forces. Explain how work is related to the total mechanical energy of a system, then use this information to set up and solve the problem above.

Please Give step by step explanation.

Answer 1

Ans: 1.89888m

A diagram of the scenario is below,

The solution can be obtained y applying work energy theorem,

It states that Change in total mechanical energy = Work done

Mechanical enegry is here the sum of kinetic() and gravitational potential energies()

So, Initial mechanical energy (Since kinetic energy is zero, rest)

Final mechanical energy (Since final potential energy is zero h=0. The zero value of potential energy can be fixed anywhere. What always concers is the change in potential energy not the exact numerical value of it at any point. So here we fix potential energy to be zero at floor)

Now work done on the body. Assuming a constant opposing force exerted by the air throughout the journey,

Workdone, (The force acts opposite to the motion of the body hence the negative sign. Work done by dissipiative forces are always negative. It covers total distance 5m throughout journey)

Thus we have our work energy theorem,

Sustituting the values