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Svetlanka [38]
3 years ago
13

The force F required to compress a spring a distance x is given by F 2 F0 5 kx where k is the spring constant and F0 is the prel

oad. Determine the work required to compress a spring whose spring constant is k 5 200 lbf/in a distance of one inch starting from its free length where F0 5 0 lbf. Express your answer in both lbf·ft and Btu.
Physics
1 answer:
IrinaVladis [17]3 years ago
6 0

Answer:

a)W=8.333lbf.ft

b)W=0.0107 Btu.

Explanation:

<u>Complete question</u>

The force F required to compress a spring a distance x is given by F– F0 = kx where k is the spring constant and F0 is the preload. Determine the work required to compress a spring whose spring constant is k= 200 lbf/in a distance of one inch starting from its free length where F0 = 0 lbf. Express your answer in both lbf-ft and Btu.

Solution

Preload = F₀=0 lbf

Spring constant k= 200 lbf/in

Initial length of spring x₁=0

Final length of spring x₂= 1 in

At any point, the force during deflection of a spring is given by;

F= F₀× kx  where F₀ initial force, k is spring constant and x is the deflection from original point of the spring.

W=\int\limits^2_1 {} \, Fds \\\\\\W=\int\limits^2_1( {F_0+kx} \,) dx \\\\\\W=\int\limits^a_b {kx} \, dx ; F_0=0\\\\\\W=k\int\limits^2_1 {x} \, dx \\\\\\W=k*\frac{1}{2} (x_2^{2}-x_1^{2}  )\\\\\\W=200*\frac{1}{2} (1^2-0)\\\\\\W=100.lbf.in\\\\

Change to lbf.ft by dividing the value by 12 because 1ft=12 in

100/12 = 8.333 lbf.ft

work required to compress the spring, W=8.333lbf.ft

The work required to compress the spring in Btu will be;

1 Btu= 778 lbf.ft

?= 8.333 lbf.ft----------------cross multiply

(8.333*1)/ 778 =0.0107 Btu.

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At room temperature, sound travels at a speed of about 344 m/s in air. You see a distant flash of lightning and hear the thunder
beks73 [17]

Answer:

d=1.67mi

Explanation:

Assuming the light takes essentially no time to reach you, the distance at which the lightning occurred can be calculated by multiplying the speed of sound by the time it takes to hear the thunder:

d=v_st\\d=344\frac{m}{s}(7.8s)\\d=2683.2m*\frac{1mi}{1609.34m}=1.67mi

4 0
3 years ago
In a crash test, a truck with mass 2100 kg traveling at 22 m/s smashes head-on into a concrete wall without rebounding. The fron
slega [8]

Answer:

a)   v_average = 11 m / s, b)  t = 0.0627 s

, c)    F = 7.37 10⁵ N

, d)   F / W = 35.8

Explanation:

a) truck speed can be found with kinematics

         v² = v₀² - 2 a x

The fine speed zeroes them

           a = v₀² / 2x

           a = 22²/2 0.69

           a = 350.72 m / s²

The average speed is

           v_average = (v + v₀) / 2

           v_average = (22 + 0) / 2

           v_average = 11 m / s

b) The average time

          v = v₀ - a t

          t = v₀ / a

          t = 22 / 350.72

          t = 0.0627 s

c) The force can be found with Newton's second law

             F = m a

             F = 2100 350.72

             F = 7.37 10⁵ N

.d) the ratio of this force to weight

             F / W = 7.37 10⁵ / (2100 9.8)

             F / W = 35.8

.e) Several approaches will be made:

- the resistance of air and tires is neglected

- It is despised that the force is not constant in time

- Depreciation of materials deformation during the crash

5 0
3 years ago
When Trinity pulls on the rope with her weight, Newton's Third Law of Motion tells us that the rope will _____.
Grace [21]
The rope will pull back against you.
5 0
3 years ago
Read 2 more answers
The largest hailstone every measured fell in Vivian, Nebraska in 2010. The circumference of that hailstone was 19 inches. Using
Crazy boy [7]

Answer:

6.04788 in

115.82654\ in^3

78.38779 m/s

0.88159 kg

34.55294 J

Explanation:

Circumference is given by

c=2\pi r\\\Rightarrow r=\dfrac{c}{2\pi}\\\Rightarrow r=\dfrac{19}{2\pi}\\\Rightarrow r=3.02394\ in

Diameter is given by

d=2r\\\Rightarrow d=2\times 3.02394\\\Rightarrow d=6.04788\ in

The diameter is 6.04788 in

6.04788\times 2.54=15.3616152\ cm

Volume of sphere is given by

v=\dfrac{4}{3}\pi r^3\\\Rightarrow v=\dfrac{4}{3}\pi 3.02394^3\\\Rightarrow v=115.82654\ in^3

The volume is 115.82654\ in^3

115.82654\times \dfrac{1}{1728}=0.06702\ ft^3

Fall velocity is given by

V=k\sqrt{d}\\\Rightarrow V=20\sqrt{15.3616152}\\\Rightarrow V=78.38779\ m/s

The velocity of the fall will be 78.38779 m/s

Mass is given by

m=\rho v\\\Rightarrow m=29\times 0.06702\\\Rightarrow m=1.94358\ lb

1.94358\ lb=1.94358\times \dfrac{1}{2.20462}=0.88159\ kg

The mass is 0.88159 kg

Kinetic energy is given by

K=\dfrac{1}{2}mv^2\\\Rightarrow K=\dfrac{1}{2}0.88159\times 78.38779\\\Rightarrow K=34.55294\ J

The kinetic energy is 34.55294 J

4 0
3 years ago
) A steel guitar string with a diameter of 1.00 mm is stretched between supports 80.0 cm apart. The temperature is 0.0°C. (a) Fi
ladessa [460]

Answer: a. Mass per unit length =0.0245kg/m

b. Tension =2.45x10^-8N

C. Tension = 2.45 x10^-8N

Fundamental frequency =200Hz

Explanation:

7 0
3 years ago
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