Air Accel

Related Products:

Air Accel
Air Accel image
Conservation of Energy?

in a homework problem. i am given a graph of gravitational potential energy versus height of a ball that has a mass of 1kg, which is thrown straight up into the air with a velocity of 16m/s. the graph is a straight line, and makes perfect sense. mgh = U and just plug in varying height to get the points. for this problem they use 10m/s^2 to be accel. due to gravity.

but then they ask me to plot a graph of the Total Energy (energy in joules versus height). and they're saying its supposed to be a constant.

how do i calculate this "total energy" constant from the information i am given?

Okay, this is conservation of energy.

From your knowledge of the world around you, you should be familiar with the fact that a falling object tends to get faster as it falls. That's because the object has both stored potential energy (mgh) and the kinetic energy, (1/2)mv^2.

In the real world, energy can be lost to many things such as friction, heat, or a drag force, but in introductory physics classes, we assume that no energy is lost in that manner; it is simply converted from PE to KE and vice versa.

At the peak of the ball's flight, all of its energy is PE, since velocity is zero thus KE is zero.

At the bottom of the ball's flight, all of its energy is KE, since H = 0, forcing PE = 0.

Use mgh at the top of the ball's flight or (1/2)mv^2 at the bottom of the ball's flight. Both should give you the same answer.

Since the height at the top is unknown, it may be best to use KE at bottom. KE = (1/2) * m * v^2 = (1/2) * (1 kg) * (16 m/s)^2 = 128 (kg*m/s/s)(m) = 128 Nm = 128 J.