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2 years ago

8

How much extra water does a 147-lb concrete canoe displace compared to an ultralightweight 38-lb kevlar canoe of the same size c

arrying the same load?

1 answer:

romanna [79]2 years ago

5 0

We use the formula, to calculate the volume of water displaced by concrete canoe,

$V =\frac{W}{\gamma }$

Here, W is the weight of concrete canoe and $\gamma$ is the specific weight of water and its value is $62.4\ lb/ft^3$ .

So,

$V =\frac{ 147\ lb}{62.4\ lb/ft^3}=2.356\ ft^3$ .

Now the volume of water occupied in ultra lightweight kevlar canoe,

$v=\frac{w}{\gamma}$

Here, w is weight of kevlar canoe.

So,

$v=\frac{38\ lb}{62.4\ lb/ft^3} =0.6089\ ft^3$

Thus, the volume of water displaced,

$=V-v=2.356\ ft^3-0.6089\ ft^3=2.19\ ft^3$ .

Hence, the volume of water displaced canoe compared to an ultra-lightweight kevlar canoe is $2.19\ ft^3$

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The flywheel in the shape of a solid cylinder of mass 75.0 kg and diameter 1.40 m rotates about an axis passing through the cent

Anni [7]

The torque required for the cylinder is 76.99 N m.

What is torque?

Torque may be defined as the product of the force and the distance perpendicular to the force from the axis of rotation.

Calculation of the angular acceleration:

The first kinematic equation for the rotational motion is,

ω=ω₀+αt

where ω₀ is the initial angular velocity, ω is the final angular velocity, α is the angular acceleration and t is the time. Since the cylinder starts from the rest, its initial angular velocity is zero.

Here, ω=320 rev/min or ω=320*2π/60 rad/sec, ω₀=0 and t=8.00 sec. Put these values in the above equation and solve it to get the value of angular acceleration.

320*2π/60=0+α*8

α=320*2π/(8*60)

α=4.19 rad/s^2

Calculation of the torque:

The torque T is given by the formula,

T=Iα

where I is the moment of inertia.

For the cylinder, I=1/2*mr^2

where m is the mass of the cylinder and r is the radius of the cylinder.

So,

T=1/2*mr^2*α

Here m=75 kg, radius r is half of the diameter r=1.4/2=0.7 m, and α=4.19 rad/s^2. Using these values in the formula of torque.

T=1/2*(75)*(0.7)^2*4.19

T= 76.99 N m

Learn more about the torque.

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6 0

1 year ago

Kieran takes off from rest down a 50 m high, 10° slope on his jet-powered skis. The skis have a thrust of 280 N parallel to the

xz_007 [3.2K]

Answer:0.46

Explanation:

Given

Initial height $h=50 m$

inclination $\theta =10^{\circ}$

Thrust $=280 N$

combined mass of kieran and skis $m=50 kg$

Speed at the bottom $v=40 m/s$

From Work Energy Theorem

Work done by all the force is equal to change in kinetic Energy

$W_{gravity}+W_{friction}+W_{thrust}=\frac{1}{2}mv^2-0$ ------------1

distance traveled along the slope $x=\frac{50}{\sin 10}=287.93 m$

$W_{gravity}=mgh=50\times 9.8\times 50=24500 J$

$W_{thrust}=F\times x=280\times 287.93=80,620.4 J$

$W_{friction}=-\mu mg\cos 10$

substitute in 1

$24,500+80,620.4+W_{friction}=\frac{1}{2}\times 50\times 1600$

$W_{friction}=40,000-24,500-80,620.4$

$-\mu \cdot 50\times 9.8\times 287.93=-65,120.4$

$\mu =\frac{65,120.4}{141,085.7}=0.46$

8 0

2 years ago

If vector A =i+2j-k and vec A cross vec B =3i-j+5k. find vec B

postnew [5]

Let <em>B</em> = <em>a</em> <em>i</em> + <em>b</em> <em>j</em> + <em>c</em> <em>k</em>. Then the cross product of <em>A</em> = <em>i</em> + 2<em>j</em> - <em>k</em> with <em>B</em> is

<em>A</em> × <em>B</em> = ( <em>i</em> + 2<em>j</em> - <em>k </em>) × ( <em>a</em> <em>i</em> + <em>b</em> <em>j</em> + <em>c</em> <em>k</em> )

<em>A</em> × <em>B</em> = <em>a</em> ( <em>i</em> × <em>i</em> ) + 2<em>a</em> ( <em>j</em> × <em>i</em> ) - <em>a</em> ( <em>k</em> × <em>i </em>)

… … … + <em>b</em> ( <em>i</em> × <em>j</em> ) + 2<em>b</em> ( <em>j </em>× <em>j</em> ) - <em>b</em> ( <em>k</em> × <em>j</em> )

… … … + <em>c</em> ( <em>i</em> × <em>k</em> ) + 2<em>c</em> ( <em>j</em> × <em>k</em> ) - <em>c</em> ( <em>k</em> × <em>k</em> )

<em>A</em> × <em>B</em> = 0 - 2<em>a</em> <em>k </em>- <em>a</em> <em>j</em>

… … … + <em>b</em> <em>k</em> + 0 + <em>b</em> <em>i</em>

… … … - <em>c</em> <em>j</em> + 2<em>c</em> <em>i</em> - 0

<em>A</em> × <em>B</em> = (<em>b</em> + 2<em>c</em>) <em>i</em> + (-<em>a</em> - <em>c</em>) <em>j</em> + (<em>b</em> - 2<em>a</em>) <em>k</em>

So we have

3 <em>i</em> - <em>j</em> + 5 <em>k </em>= (<em>b</em> + 2<em>c</em>) <em>i</em> + (<em>c</em> - <em>a</em>) <em>j</em> + (<em>b</em> - 2<em>a</em>) <em>k</em>

which gives us the system of equations,

{ <em>b</em> + 2<em>c</em> = 3

{ -<em>a</em> - <em>c</em> = -1

{ -2<em>a</em> + <em>b</em> = 5

Solve for <em>a</em>, <em>b</em>, and <em>c</em>.

• Eliminate <em>c</em> from the first two equations:

(<em>b</em> + 2<em>c</em>) + 2 (-<em>a</em> - <em>c</em>) = 3 + 2 (-1)

-2<em>a</em> + <em>b</em> = 1

But -2<em>a</em> + <em>b</em> = 5, and 5 ≠ 1, so there is no such vector <em>B</em> that satisfies the cross product!

8 0

2 years ago

The small metal cylinder has a mass of 0.20 kgkg, the coefficient of static friction between the cylinder and the turntable is 0

deff fn [24]

Answer:

velocity of the metal cylinder = 0.343 m/s

Explanation:

Force putting the metal cylinder is given by

F = mv²/r

But this force will balance the frictional force between the metal cylinder and the turntable

The frictional force is given by

μN = μ × mg = 0.08 × 0.2 × 9.81 = 0.15696 N

r = 0.15 m, m = 0.2 kg,

F = mv²/r = 0.2 v²/(0.15) = 1.3333 v²

1.3333 v² = 0.15696

v² = 0.117

v = 0.343 m/s

8 0

3 years ago

Within a period of the periodic table, how do the properties of the elements vary?

Nonamiya [84]

Answer:

Elements in the same period have the same number of electron shells; moving across a period (so progressing from group to group), elements gain electrons and protons and become less metallic. This arrangement reflects the periodic recurrence of similar properties as the atomic number increases.

Explanation:

The Periodic Table can predict the properties of new elements, because it organizes the elements according to their atomic numbers. ... They hope that the two nuclei at the centre of these atoms will fuse and form a heavier nucleus. When these heavy elements form, they are usually highly unstable.

5 0

3 years ago