Ask question

Ask question

All categories

3 years ago

7

A person is planning a bungee jump from a 40 meter high bridge. Under the bridge is a river with crocodiles, so the person does

not want to be submerged into the water. The rubber rope fastened to the ankles has a spring constant of 3,600 N/m per meter length. Thus one meter length of rope will have a spring constant of 3,600 N/m, two meters of rope will have a spring constant of 1,800 N/m, three meters of rope will have a spring constant of 1,200 N/m and so forth. The distance from the ankles to the top of the head is 175 cm, and the person has a mass of 80 kg. Calculate: a. b. c. how long the rope should be [m] how much deflection the rope experiences [m] how much impact force the bungee jumper experiences [N]

1 answer:

Nonamiya [84]3 years ago

3 0

Answer:

a. l = 19.7m, b. 18.55m, c. Impact Force = 3889.84 N

Explanation:

The total energy of the system when the person is at top of the bridge is

Potential energy = mgh, Kinetic energy = 0

The total energy of the system when the person reaches just above the surface

Potential energy = 0, Kinetic energy = 0, Spring energy = ½ K X2, where k is the spring constant and X is the deflection

Applying conservation of energy

mgh = 0 + 0 + ½ K X²

80 x 9.81 x 40 = ½ (3600/l) X²

31392 = ½ (3600/l) X²

We can also conclude that

l+ X + 1.75 = 40

l + X = 38.25

a. <u>Substitute the value of x from above into the energy conversion expression</u>

31392 = ½ (3600/l)(38.25 - l)²

31392 x 2/3600 = (38.25 + l² – 2l(38.25))/l

17.44l = l2 – 76.5l + 38.25²

l² – 76.5l – 17.44l +1463.0625 = 0

Solving for l we get

L = 19.7

Hence, length of the rope is 19.7m

b. <u>The deflection is calculated by using the relation between l and X</u>

L + X = 38.25

X = 38.25 – 19.7 = 18.55m

c. <u>The impact force is calculated using the impact force formula which relates the impact force with the deflection</u>

F = KX

F = (3600/l) . X

F = (3600/19.7) . (18.55) = 3889.84 N

Thus, the impact force is 3889.84 N

You might be interested in

Which reference source may be consulted to answer questions regarding the Professional Engineers Act?

9966 [12]

Answer: c. The Professional Engineers Act and Board Rules

Explanation:

The reference source may be consulted to answer questions regarding the Professional Engineers Act is the The Professional Engineers Act and Board Rules.

The Professional Engineers Act and Board Rules is an Act that was established in order to regulate the qualifications for professional engineered, register them and also make sure that their conducts and behavior are looked into.

6 0

3 years ago

A fluid with a relative density of 0.9 flows in a pipe which is 12 m long and lies at an angle of 60° to the horizontal At the t

Minchanka [31]

Answer:

$Q=7.3\times 10^{-3} m^3/s$

Explanation:

Given that

At top $d_2=30 mm,P_2=860 KPa ,P_1=1000 KPa,d_1=85 mm$

$\rho =900\dfrac{Kg}{m^3}$

We know that

$\dfrac{P_1}{\rho g}+\dfrac{V_1^2}{2g}+Z_1=\dfrac{P_2}{\rho g}+\dfrac{V_2^2}{2g}+Z_2$

$A_1V_1=A_2V_2$

$\frac{V_1}{V_2}=\left(\dfrac{d_2}{d_1}\right)^2$

$\frac{V_1}{V_2}=\left(\dfrac{30}{85}\right)^2$

$V_2=8.02V_1$

$Z_2=12 sin60^{\circ}$

$\dfrac{1000\times 1000}{900\times 9.81}+\dfrac{V_1^2}{2\times 9.81}+0=\dfrac{860\times 1000}{900\times 9.81 }+\dfrac{V_2^2}{2\times 9.81}+12 sin60^{\circ}$

So $V_1=1.30$ m/s

We know that flow rate Q=AV

$Q=A_1V_1$

By putting the values

$A_1=\dfrac{\pi}{4}d^2$

$Q=7.3\times 10^{-3} m^3/s$

To find the flow rate we do not need the direction of flow,because we are just doing balancing of energy at inlet and at the exits of pipe.

4 0

3 years ago

The ____ neurons allow the body to move and are greatly influenced by electri

LuckyWell [14K]

The Neurons allow the body to move
A

7 0

3 years ago

Read 2 more answers

The pump of a water distribution system is powered by a 15-kW electric motor whose efficiency is 90 percent. The water flow rate

wariber [46]

Answer:

Mechanical power of pump is 74.07%.

Explanation:

Power of motor = 15 KW

Efficiency of motor= 90%

So the actual power(P) supplied by motor = 0.9 x 15 KW

P=13.5 KW

Water flow rate = 50 L/s

Volume flow rate = 50 L/s

We know that

$1000\ L/s=1\ m^3/s$

So

$Volume\ flow \rate =0.05\ m^3/s$

We know that pump is an open system and work input for open system can be calculated as

W=VΔP

ΔP is the pressure difference

V is the volume flow rate

So by putting the values

W=0.05 (300-100) (here ΔP=300 - 100=200 KPa)

W=10 KW

So mechanical power of pump

$\eta =\dfrac{W}{P}$

$\eta =\dfrac{10}{13.5}$

η =0.7407

Mechanical power of pump is 74.07%.

6 0

3 years ago

Gemiola [76]

Answer:

The correct option is;

Fluid power systems are much more efficient with regards to energy costs and overall cost savings

Explanation:

The option that will provide a valid reason for the larger proportion of the consumers to change to the fluid power trucks from the diesel powered trucks is the possibility of increased efficiency in the cost of energy, and the cost savings to be made from making the switch to the fluid power trucks, due to the lower input required and the faster rate at which the consumer budget will be rebalanced leading to increased return on investment and improved rate of return.

5 0

3 years ago