Lab 10: Conservation of Energy

A projectile (m=10kg) is launched from ground level at an angle of 50° above the horizontal with an initial speed of 55 m/s. Assume the ground under the projectile is perfectly flat throughout the projectile’s flight.

If we ignore air resistance and assume the projectile stays relatively close to the surface of the Earth, the acceleration of the projectile in the horizontal (x) and vertical (y) directions is constant:

ax=0 and ay=g=9.8 m/s2 downwards

Fill in the table on the left using t=0.5 s as the time interval for the following variables:

vx (velocity in horizontal direction)

vy (velocity in vertical direction)

v (speed of the projectile)

y (height of the projectile)

K (kinetic energy)

Ug (gravitational potential energy)

ME (total mechanical energy)

vx, vy ,and y can be found directly from the kinetic equations for constant acceleration and $v=√(vx^2+vy^2)$. See Lab #3 for details.

Note: when y<0, the object has already hit the ground.

Kinetic energy is an object’s energy due to it’s motion. As an equation,

$K=1/2mv2$

Gravitational potential energy is the stored energy of an object due to it’s relative position in a gravitational field. If we define the ground to have

zero potential energy (our zero reference level), the gravitational potential energy of an object a distance ‘y’ above the ground can be written as

Ug=mgy

The total mechanical energy of an object is the sum of the kinetic plus the potential energies (ME=K+Ug). If the forces acting on an object are conservative the total mechanical energy is time invariant (constant).

Make a graph showing the kinetic and gravitational potential energy of the projectile as a function of time (on the same graph), from when it is launched until it hits the ground. Include the total mechanical energy as a function of time on your graph as well.

What can we conclude about the total mechanical energy? Therefore, what can we say about the force of gravity?

The total mechanical energy is constant. Therefore the force of gravity is a conservative force.

At what point or points (launch, apex, or landing) is the kinetic energy of the projectile greatest and least?

The kinetic energy is maximum at launch and landing. It is minimum at the apex (highest point of trajectory).

At what point or points (launch, apex, or landing) is the potential energy of the projectile greatest and least?

The potential energy is minimum (zero) at launch and landing. It is maximum at apex (highest point of trajectory).

Does the momentum of the projectile change during it’s flight? Does the magnitude of the momentum change? Explain.

Since there is a force on the projectile (the gravitational force downward) the total momentum is changing. Since this force is constant the total momentum decreases liniar with time from the launch until the landing. The magnitude (module of momentum) also decreases liniar with time from launch until apex then increases liniar with time until landing.

t (s) | v_{x} (m/s)v_{x} (m/s) |
v_{y} (m/s)v_{y} (m/s) |
v (m/s) | y (m) | K (J) | U_{g} (J)U_{g} (J) |
ME (J) |

0 | 35.35 | 42,13 | 55,00 | 0,00 | 15125 | 0 | 15125 |

0,5 | 35.35 | 37,23 | 51,34 | 19,84 | 13179 | 1944 | 15123 |

1 | 35.35 | 32,33 | 47,90 | 37,23 | 11472 | 3649 | 15125 |

1,5 | 35.35 | 27,43 | 44,74 | 52,17 | 10008 | 5113 | 15121 |

2 | 35.35 | 22,53 | 41,91 | 64,66 | 8782 | 6337 | 15119 |

2,5 | 35.35 | 17,63 | 39,50 | 74,70 | 7801 | 7321 | 15122 |

3 | 35.35 | 12,73 | 37,57 | 82,29 | 7058 | 8064 | 15122 |

3,5 | 35.35 | 7,83 | 36,20 | 87,43 | 6552 | 8568 | 15120 |

4 | 35.35 | 2,93 | 35,47 | 90,12 | 6291 | 8832 | 15123 |

4,5 | 35.35 | -1,97 | 35,40 | 90,36 | 6266 | 8855 | 15121 |

5 | 35.35 | -6,87 | 36,01 | 88,15 | 6484 | 8639 | 15123 |

5,5 | 35.35 | -11,77 | 37,25 | 83,49 | 6938 | 8182 | 15120 |

6 | 35.35 | -16,67 | 39,08 | 76,38 | 7636 | 7485 | 15121 |

6,5 | 35.35 | -21,57 | 41,41 | 66,82 | 8574 | 6548 | 15122 |

7 | 35.35 | -26,47 | 44,16 | 54,81 | 9750 | 5371 | 15121 |

7,5 | 35.35 | -31,37 | 47,26 | 40,35 | 11168 | 3954 | 15122 |

8 | 35.35 | -36,27 | 50,65 | 23,44 | 12827 | 2297 | 15124 |

8,5 | 35.35 | -41,17 | 54,26 | 4,08 | 14721 | 400 | 15121 |

9 | 35.35 | 0,00 | 35,35 | 0,00 | 6248 | 0 | 6248 |