Write the Energy Equation

In each case your equation will involve mass, distance, velocity and g. Show the distance(s) in a sketch. Do not look at the answers until you have written the equations. Figure out how to write the initial energy Eo, then the total work SW, if any, and be sure to get the signs right on the W’s: helping is + and hindering is -.  Then write the expression for final energy E, and write

Eo + SW = E
 in terms of the various velocities, distances, forces, etc.

 

1. The cart coasts from rest down the hill; no friction.

2. Same as # 1 but with initial v = vo.

3. Same as # 2 but with average friction force f while traveling distance s.

4. Glider on air track, vo = 0, no friction, travels uphill, tilt angle q from horizontal. Masses m&M


5. Same as # 4 but with coefficient of kinetic friction = m  between glider and track.

6. Same as # 4 but lower the left end so it goes downhill at angle q from horizontal.

7. A projectile has speed v1 at height h1 and speed v2 at height h2.

8. While a car goes up a hill, the engine does work W and the total losses of energy due to friction, etc., have absolute value Wf.

The following problems have a spring with spring constant k.

9. Glider on level air track: spring stretched x, vo = 0, velocity v when it reaches the relaxed position.

10. Same as # 9 but it goes uphill, tilt angle q from horizontal.

11. A bungee jumper falls distance h before the bungee cord offers any resistance, then travels an additional distance y before v = 0 (momentarily).

12. In problem 11, the velocity is v when the cord is half stretched.

SOLUTIONS

1.mgh = ½mv2
2. ½mvo2 + mgh = ½mv2
3. ½mvo2 +mgh -fs = ½mv2
4. mgd = Mgdsinq + ½(m+M)v2
5. mgd - m Mgdcosq = Mgdsinq +½(m+M)v2
6. mgd + Mgdsinq = ½(m+M)v2
7. ½mv12 + mgh1 = ½mv22 + mgh2
8. ½mvo2 + W - Wf = mgy + ½mv2
9. ½kx2 = ½mv2
10. ½kx2 = ½mv2 + mgxsinq
11. mg(h+y) = ½ky2
12. mg(h+y/2) = ½k(y/2)2 + ½mv2

go back to work and energy.

Or go to one of the main physics pages:
Mechanics
Fluids, heat, electricity and magnetism
Vibrations and waves
Quantum
Index

comments, questions: email me-  fredrick.gram at tri-c.edu (remove spaces and replace at with @.