Equation need answers not quite sure

A tightrope walker wants to know the tension used to support the rope that is suspended between two poles. The rope is 18 m long

Alla [95]

Answer:

T = 29.6 N

Explanation:

length of the rope is

L = 18 m

mass of the rope is

m = 12 kg

now we have

mass per unit length of the rope is given as

[te]\lambda = \frac{12 kg}{18 m}[/tex]

now time taken by wave to reach from end to other

$t = \frac{L}{v}$

$2.7 s = \frac{18}{v}$

$v = 6.67 m/s$

now we have

$v = \sqrt{\frac{T}{\lambda}}$

$6.67 = \sqrt{\frac{T}{0.67}}$

so we will have

$T = 29.6 N$

5 0

4 years ago

In a car lift used in a service station, compressed air exerts a force on a small piston of circular cross section having a radi

Vitek1552 [10]

Answer:

(a) 1,569.63 N

(b) 195,933.99 Pa

(c) As pressure and volume are equal for each piston, workdone must also be equal

(d) 1,647.47 kg

Explanation:

Let the cross-sectional area (CSA) of small piston = A₁

Let the cross-sectional area (CSA) of the bigger piston = A₂

Let the Force applied at the smaller piston = F₁

Let the Force applied at the bigger piston = F₂

The principle of hydraulic lift assumes the that the fluid is in-compressible, resulting to a constant pressure system.

F₁/A₁ =F₂/A₂----------------------------------------------------------- (1)

(a) F₁= F₂ xA₁ /A₂

F₂ = 13,300 N

A₁ = π r₁²

=π x (0.0505)²

= 0.008011 m²

A₂= π r₂²

=π x (0.147)²

= 0.06788 m²

Substituting into (1)

F₁ = 13,300 x 0.008011/0.06788

= 1,569.6272

≈ 1,569.63 N

(b) Air pressure = Force/Area

= F₁/A₁

= 1,569.6272/ 0.008011

= 195,933.99 Pa

(c) The pressure is constant for both pistons according to Pascal Law.

Workdone = force x distance----------------------------------------- (2)

force = pressure × area

distance = volume/area from

Substituting into (2)

Workdone = pressure × volume.

As pressure and volume are equal for each piston, work must also be equal

(d) F₂ = F₁ x A₂/ A₁---------------------------------------------------- (3)

A₁ = π r₁²

=π x (0.079)²

= 0.01960 m²

A₂= π r₂²

=π x (0.353)²

= 0.3914 m²

Substituting into (2)

F₂= 825 x 0.3914/ 0.01960

= 16,474.7448

≈ 16,474.74 N

= 1,647.47 kg

3 0

3 years ago

A car of mass 1000.0 kg is traveling along a level road at 100.0 km/h when its brakes are applied. Calculate the stopping distan

OleMash [197]

Explanation:

It is given that,

Mass of the car, m = 1000 kg

Speed of the car, v = 100 km/h = 27.77 m/s

The coefficient of kinetic friction of the tires, $\mu_k=0.5$

Let f is the net force acting on the body due to frictional force, such that,

$-f=ma$

$a=\dfrac{-f}{m}$

$a=\dfrac{-\mu _k mg}{m}$

$a=\mu_k g$

$a=-0.5\times 9.8$

$a=-4.9\ m/s^2$

We know that the acceleration of the car in calculus is given by :

$v.dv=a.dx$ , x is the stopping distance

$\int\limits^0_v {v.dv}=\int\limits^x_0 {a.dx}$

$\dfrac{v^2}{2}|_v^0=ax$

$0-(27.77)^2=-2\times 4.9x$

On solving the above equation, we get, x = 78.69 meters

So, the stopping distance for the car is 78.69 meters. Hence, this is the required solution.

6 0

3 years ago

A transformer consists of 340. primary windings and 980. secondary windings. If the emf of the primary coil is 30.0 V, what is t

xxTIMURxx [149]

Answer:

86.47 V

Explanation:

It will be multiplied by the ratio of the windings

980/340 * 30 = 86.47 v

4 0

2 years ago

A leopard chasing a deer reaches a constant speed of 75m / s. In How long does 1200m travel?

xxTIMURxx [149]

Answer:

16 seconds

Explanation:

To do this you would set up the equation 75x=1200. Then you would divide 75 from both sides so you get x=16 or it takes 12 seconds for it to travel 1200 meters

6 0

4 years ago

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