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3 years ago

2. A carpenter tosses a shingle off a 9.4 m high roof, giving it an initial horizontal

1 answer:

8 0

Sounds like the shingle/ball is thrown from the roof horizontally, so that the distance it travels x after time t horizontally is

x = (7.2 m/s) t

The object's height y at time t is

y = 9.4 m - 1/2 gt²

where g = 9.80 m/s² is the magnitude of the acceleration due to gravity, and its vertical velocity is

v = -gt

(a) The object hits the ground when y = 0:

0 = 9.4 m - 1/2 gt²

t² = 2 * (9.4 m) / (9.80 m/s²)

t ≈ 1.92 s

at which time the object's vertical velocity is

v = -g (1.92 s) = -18.8 m/s ≈ -19 m/s

(b) See part (a); it takes the object about 1.9 s to reach the ground.

(c) The object travels a horizontal distance of

x = (7.2 m/s) * (1.92 s) ≈ 13.8 m ≈ 14 m

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A mass MM uniform solid cylinder of radius RR and a mass MM thin uniform spherical shell of radius RR roll without slipping. If

vampirchik [111]

Answer:

vcyl / vsph = 1.05

Explanation:

The kinetic energy of a rolling object can be expressed as the sum of a translational kinetic energy plus a rotational kinetic energy.
The traslational part can be written as follows:

$K_{trans} = \frac{1}{2}* M* v_{cm} ^{2} (1)$

The rotational part can be expressed as follows:

$K_{rot} = \frac{1}{2}* I* \omega ^{2} (2)$

where I = moment of Inertia regarding the axis of rotation.
ω = angular speed of the rotating object.
If the object has a radius R, and it rolls without slipping, there is a fixed relationship between the linear and angular speed, as follows:

$v = \omega * R (3)$

For a solid cylinder, I = M*R²/2 (4)
Replacing (3) and (4) in (2), we get:

$K_{rot} = \frac{1}{2}* \frac{1}{2} M*R^{2} * \frac{v_{cmc} ^{2}}{R^{2}} = \frac{1}{4}* M* v_{cmc}^{2} (5)$

Adding (5) and (1), we get the total kinetic energy for the solid cylinder, as follows:

$K_{cyl} = \frac{1}{2}* M* v_{cmc} ^{2} +\frac{1}{4}* M* v_{cmc}^{2} = \frac{3}{4}* M* v_{cmc} ^{2} (6)$

Repeating the same steps for the spherical shell:

$I_{sph} = \frac{2}{3} * M* R^{2} (7)$

$K_{rot} = \frac{1}{2}* \frac{2}{3} M*R^{2} * \frac{v_{cms} ^{2}}{R^{2}} = \frac{1}{3}* M* v_{cms}^{2} (8)$

$K_{sph} = \frac{1}{2}* M* v_{cms} ^{2} +\frac{1}{3}* M* v_{cms}^{2} = \frac{5}{6}* M* v_{cms} ^{2} (9)$

Since we know that both masses are equal each other, we can simplify (6) and (9), cancelling both masses out.
And since we also know that both objects have the same kinetic energy, this means that (6) are (9) are equal each other.
Rearranging, and taking square roots on both sides, we get:

$\frac{v_{cmc}}{v_{cms}} =\sqrt{\frac{10}{9} } = 1.05 (10)$

This means that the solid cylinder is 5% faster than the spherical shell, which is due to the larger moment of inertia for the shell.

3 0

3 years ago

Question 5 (2 points)

Radda [10]

Answer:

Increase the work being done or decrease the time in which the work is completed

Explanation:

I got it right on the quiz i just took :)

5 0

3 years ago

The mechanical advantage of a wheel and axle is the radius of the wheel divided by the radius of the axle. TRUE or FALSE.

viva [34]

True! The mechanical advantage of the wheel and axle is equal to the ratio of the radius of the wheel over the radius of the axle.

4 0

3 years ago

What are gamma rays and what are its uses??

sukhopar [10]

"Gamma rays" is the name that we call the shortest of all electromagnetic waves. They're shorter than radio waves, microwaves, infrared waves, heat waves, visible light waves, ultraviolet waves, and X-rays. They extend all the way down to waves that are as short as the distance across an atom.

Being so short, they carry lots of energy. They can penetrate many materials, and they can damage living cells and DNA. They're dangerous.

The sun puts out a lot of gamma radiation. The atmosphere (air) filters out a lot of it, otherwise there couldn't even be any life on Earth.

As soon as astronauts fly out of the atmosphere, they need a lot of shielding from gamma rays.

You know the precautions we take when we're around X-rays. The same precautions apply around gamma rays, only a lot more so.

It's only in the past several years that we've learned how to MAKE gamma rays without blowing things up. Also, how to control them, and how to use them for medical and industrial applications.

3 0

2 years ago

What is the force required to produce an acceleration of 46.4

Brilliant_brown [7]

That depends on the mass of the object, and the unit of the '46.4' .

If the '46.4' is ' meters per second² ' , then the force required is

(mass of the object in kilograms) x (46.4) newtons .

7 0

3 years ago