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Monica [59]
1 year ago
13

B. A hydraulic jack has a ram of 20 cm diameter and a plunger of 3 cm diameter. It is used for lifting a weight of 3 tons. Find

the force required at the plunger.
a. 675.2kgf

b. 67.52kgf

c. 6752.0kgf

d. None of the above
Physics
1 answer:
lozanna [386]1 year ago
4 0

Answer:

option (b)

Explanation:

According to the Pascal's law

F / A = f / a

Where, F is the force on ram, A be the area of ram, f be the force on plunger and a be the area of plunger.

Diameter of ram, D = 20 cm, R = 20 / 2 = 10 cm

A = π R^2 = π x 100 cm^2

F = 3 tons = 3000 kgf

diameter of plunger, d = 3 cm, r = 1.5 cm

a = π x 2.25 cm^2

Use Pascal's law

3000 / π x 100 = f / π x 2.25

f = 67.5 Kgf

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A section of highway has the following flowdensity relationship q = 50k − 0.156k2 [with q in veh/h and k in veh/mi]. What is the
lions [1.4K]

Answer:

a) capacity of the highway section = 4006.4 veh/h

b) The speed at capacity = 25 mph

c) The density when the highway is at one-quarter of its capacity = k = 21.5 veh/mi or 299 veh/mi

Explanation:

q = 50k - 0.156k²

with q in veh/h and k in veh/mi

a) capacity of the highway section

To obtain the capacity of the highway section, we first find the k thay corresponds to the maximum q.

q = 50k - 0.156k²

At maximum flow density, (dq/dk) = 0

(dq/dt) = 50 - 0.312k = 0

k = (50/0.312) = 160.3 ≈ 160 veh/mi

q = 50k - 0.156k²

q = 50(160.3) - 0.156(160.3)²

q = 4006.4 veh/h

b) The speed at the capacity

U = (q/k) = (4006.4/160.3) = 25 mph

c) the density when the highway is at one-quarter of its capacity?

Capacity = 4006.4

One-quarter of the capacity = 1001.6 veh/h

1001.6 = 50k - 0.156k²

0.156k² - 50k + 1001.6 = 0

Solving the quadratic equation

k = 21.5 veh/mi or 299 veh/mi

Hope this Helps!!!

3 0
2 years ago
An object at rest is suddenly broken apart into two fragments by an explosion one fragment acquires twice the kinetic energy of
satela [25.4K]
<span>First, we use the kinetic energy equation to create a formula: Ka = 2Kb 1/2(ma*Va^2) = 2(1/2(mb*Vb^2)) The 1/2 of the right gets cancelled by the 2 left of the bracket so: 1/2(ma*Va^2) = mb*Vb^2 (1) By the definiton of momentum we can say: ma*Va = mb*Vb And with some algebra: Vb = (ma*Va)/mb (2) Substituting (2) into (1), we have: 1/2(ma*Va^2) = mb*((ma*Va)/mb)^2 Then: 1/2(ma*Va^2) = mb*(ma^2*Va^2)/mb^2 We cancel the Va^2 in both sides and cancel the mb at the numerator, leving the denominator of the right side with exponent 1: 1/2(ma) = (ma^2)/mb Cancel the ma of the left, leaving the right one with exponent 1: 1/2 = ma/mb And finally we have that: mb/2 = ma mb = 2ma</span>
8 0
2 years ago
While ice skating, you unintentionally crash into a person. Your mass is 60 kg, and you are traveling east at 8.0 m/s with respe
kaheart [24]

Answer:

6.18 m/s

Explanation:

Roller skate collision

The final direction of the system (me=M + person=P) velocity vector is at an angle; Ф, to the direction running south to north. Apply the component form of the impulse-momentum equation, firstly;

x-axis component form (+x east);

P_{Miy} + p_{Piy} + j_{y}= P_{Mfy} +P_{pfy}

m_{Mu_{Miy}+ m_{pu_{piy}}+0=(m_{M}+m_{p})V_{f} sinФ

60 ·8 + 0 = (60 + 80)V_{f}sinФ

480 = 140V_{f} sinФ................. (I)

y-axis component form (+y north);

P_{Mix} + p_{Pix} + j_{x} = P_{Mfx}+ P_{pfx}

m_{Mu_{Mix}+ m_{pu_{pix}}+0=(m_{M}+m_{p})V_{f} cosФ

0 + 80.9 = (60 + 80)V_{f}cosФ

 720= 140V_{f}cosФ

140Vf=\frac{720}{cos}Ф......................................(2)

 Substituting (2) into (1) to give the angle;

 480 = 720tan Ф

Ф = arctan(0.67) =33.69°.......................(3)

Evaluating (1) with (3) gives the velocity magnitude

480 = 140Vfsin 33.69°

Vf=6.18 m/s

note 1:

This angle corresponds to a direction; 90° - 33.69° = 56.31° north of east.

 

7 0
2 years ago
When you skid to a stop on your bike, you can significantly heat the small patch of tire that rubs against the road surface. Sup
Wittaler [7]

Answer:

W_f = 148.17J

Explanation:

During the exchange of applied force, thermal energy is generated by the friction that exists between the ground and the tire.

Said force according to the statement is the reaction of half the force on the rear tire. In this way the normal force acted is,

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The work done is given by the friction force and the distance traveled,

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The thermal energy released through the work done is,

W_f = 148.17J

3 0
2 years ago
The speed of light in benzene is 2.00×108 m/s. what is the index of refraction of benzene?
Klio2033 [76]
The index of refraction of a material is the ratio between the speed of light in vacuum, c, and the speed of light in that material, v:
n= \frac{c}{v}
where the speed of light in vacuum is c=3 \cdot 10^8 m/s. The speed of light in benzene is v=2.00 \cdot 10^8 m/s, so we can use the previous relationship to find the refractive index of benzene:
n= \frac{3 \cdot 10^8 m/s}{2.00 \cdot 10^8 m/s}=1.5
7 0
2 years ago
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