ENGR 123 Homework 5
1. How much energy is stored in the spring before the gun is fired?
Displacement [in] Force [lbf]
work [lbf in]
0
2.328
0.2
3.1
0.4
4.03
0.6
4.69
0.8
5.57
1
6.37
=0.5*(F8F7)*(G7+G8)
0
0.5428
0.713
0.872
1.026
1.194
total work [lbf in] total work [lbf ft]
0
0
0.5428
0.045233333
1.2558
0.10465
2.1278
0.177316667
3.1538
0.262816667
4.3478
0.362316667
=I7+H8
∆ E=Q+W, since Q=0
(E initial-E final) =Ws, (Einitial-0) =.362 ft lbf, E initial=.362 lbf ft
Before the trigger is pulled there is .362 lbf ft stored in the spring.
2. How fast will the dart be traveling (ft/s) when it leaves the muzzle?
Ws=.5mv2
0.362316667 lbf ft=.5(.002 lbm) v2
362.31661 lbf ft/ lbm=v2
362.31661 lbf ft/ lbm (32.2 lbm ft/ lbf s2) =11666.59484 ft2/ s2 =v2
108 ft/s=v
The instant the dart leaves the muzzle the dart is traveling at 108 ft/s.
3. How high will the dart travel based on your model?
.5v2=ghmax
(.5) 11666.59484 ft2/ s2= 32.2 ft/ s2 hmax
181 ft= hmax
The model projects that the dart will travel 181 ft in the air.
=I8/12
4. What is the percent difference between the theoretical height and the measured height?
Trial
h max actual [ft]
1
2
3
4
5
6
7
8
9
10
h max actual avg. [ft]
31
30
32
29
28
30
30
31
29
28
29.8
(181.2 ft-29.8 ft)/29.8 ft=
508%
5. Why do these two values differ?
In reality nerf darts aren’t impervious to drag so our model shows a much faster dart.