# Work and Energy - Mission WE10 Detailed Help

 In an amusement park ride, a 400-kg suspended car starts from rest at ground level (A) and is accelerated across a level section of track and then ascends a steep hill to a peak height of 40 meters (B) before coasting back towards its original position. Use g = 10 N/kg to perform an energy analysis and fill in all the blanks. (Note: Your numbers were randomly selected and likely different from the numbers listed here.)
 Work - Mechanical Energy Relationships: If non-conservative forces do net work upon an object, then the total mechanical energy of that object is changed. The sum of the kinetic and potential energies will change as work is done upon the object. The amount of work done on the object by non-conservative forces is equal to the amount of change in mechanical energy.
 Like all questions in this mission, the work done by non-conservative forces must be related to the changes in energy of the object (see Know the Law section). In the case of the car, the kinetic energy equation (see Formula Frenzy section) can be used to determine the initial and final kinetic energy of the car. It is explicitly stated that the car starts at rest; and it can be concluded that the car has a zero velocity when it has reached its peak height. The potential energy equation (see Formula Frenzy section) can be used to determine the initial and final potential energy of the car. Since the car is initially at ground level, the height and potential energy can be regarded as zero. The final height of the car is given. There is a difference between the initial and the final amount of total mechanical energy (KE + PE). The change in mechanical energy is caused by and equal to the work done upon the object. By calculating the change, the work can be determined.
 The amount of kinetic energy (KE) possessed by an object depends upon its mass (m) and its velocity (v). The formula is   KE = 0.5 • m • v2 The amount of potential energy (PE) possessed by an object depends upon its mass (m) and its height (h). The formula is    PE = m • g • h   where g is the gravitational field strength (9.8 N/kg on Earth).