Ask question

Ask question

All categories

15 days ago

13

The figure above represents a stick of uniform density that is attached to a pivot at the right end and has equally spaced marks

along its length. Any one or a combination of the four forces shown can be exerted on the stick as indicated. All four forces are exerted on the stick that is initially at rest. What is the angular momentum of the stick after 2.0s ?

1 answer:

Sav [1K]15 days ago

5 0

Answer:

After a duration of 2.0 seconds, the angular momentum of the system is $L= 2(4A+3B+2C+D)x$ .

Explanation:

Let’s denote the forces acting on the rod as A, B, C, and D, and the distance between them as $x$ .

The torque produced by force A can be expressed as

$\tau_a = 4Ax$ ,

for force B the torque is

$\tau_b = 3Bx$ ,

the torque for force C is

$\tau_c = 2Cx$ ,

and the torque due to force D is

$\tau_d = Dx$ .

This leads to a total torque on the stick as

$\tau_{tot} =\tau_a+\tau_b+\tau_c+\tau_d$

$\tau_{tot} =4Ax+3Bx+2Cx+Dx$

$\tau_{tot} =x(4A+3B+2C+D)$

Subsequently, this torque results in an angular acceleration $\alpha$ in accordance with the formula

$I \alpha = \tau_{tot}$

where $I$ represents the moment of inertia of the stick, which has a value of

$I = \dfrac{1}{3} m(4x)^2$ .

Thus, the angular acceleration calculates to

$\alpha = \dfrac{\tau_{tot} }{I}$

$\alpha =\dfrac{x(4A+3B+2C+D)}{\dfrac{1}{3}m(4x)^2 }$

$\boxed{\alpha =\dfrac{3(4A+3B+2C+D)}{16mx } .}$ .

Now, the angular momentum $L$ of the rod is given by

$L = I\omega$ ,

where $\omega$ is considered the angular velocity.

Given $\omega = \alpha t$ , we conclude that

$L = \dfrac{1}{3}m (4x)^2 *\dfrac{3(4A+3B+2C+D)}{16mx }* t$

$L= (4A+3B+2C+D)x t$

Thus, $t = 2.0s$ , the angular momentum is

$\boxed{ L= 2(4A+3B+2C+D)x. }$

You might be interested in

A champion athlete can produce one horsepower (746 W) for a short period of time. The number of 16-cm-high steps a 70-kg athlete

Sav [1095]

Answer:

407 steps

Explanation:

Based on the question,

P = mgh/t........... Equation 1

Where P stands for power, m is mass, g denotes gravity, h is height, and t represents time.

Rearranging the equation to solve for h, we have:

h = Pt/mg............. Equation 2

Providing values: P = 746 W, t = 1 minute = 60 seconds, m = 70 kg.

Given constant: g = 9.8 m/s²

By substituting into equation 2

h = 746(60)/(70×9.8)

h = 44760/686

h = 65.25 m

h = 6525 cm

Calculating number of steps: 6525/16

The resulting number of steps = 407 steps

6 0

9 days ago

A window washer on a hanging platform cleans the outside of windows on a skyscraper. The washer hoists the platform up the side

kicyunya [1011]

Answer:

The acceleration of the platform is - 1.8 m/s²

Explanation:

The net force on a body causes that body to accelerate in the direction of the resultant force applied.

Setting up the force equilibrium for the configuration:

ma = 800 - mg

100a = 800 - 100×9.8

100a = - 180

100a = - 180

a = - 1.8 m/s²

This indicates that the body is falling downward.

6 0

8 days ago

The amount of electric energy consumed by a 60.0-watt lightbulb for 1.00 minute could lift a

Sav [1095]

Answer:

Explanation:

For a 60W light bulb used for 1 minute:

P = 60 W

t = 1 minute = 60 seconds

This energy is capable of lifting an object weighing 10N.

W = 10N

This indicates conversion of electrical energy into potential energy.

Let's calculate the electrical energy:

Power describes the rate of work done.

Power = Work / time

Thus, work = power × time

Work = 60 × 60

Work = 3600 J

Potential energy calculation:

P.E = mgh

Where the weight is given by:

W = mg

Therefore, P.E = W·h

P.E = 10·h

Thus, we equate:

Potential energy = Electrical energy

P.E = Work

10·h = 3600

Dividing both sides by 10 gives:

h = 3600 / 10

h = 360m

The object can be lifted to a height of 360m.

6 0

6 days ago

A delivery man starts at the post office, drives 40 km north, then 20 km west, then 60 km northeast, and finally 50 km north to

Yuliya22 [1153]

assuming north-south is along the Y-axis and east-west along the X-axis

X = total X-displacement

from the graph, total displacement in the X-direction is computed as

X = 0 - 20 + 60 Cos45 + 0

X = 42.42 - 20

X = 22.42 m

Y = total Y-displacement

from the graph, total displacement in the Y-direction is computed as

Y = 40 + 0 + 60 Sin45 + 50

Y = 90 + 42.42

Y = 132.42 m

To calculate the magnitude of the net displacement vector, we apply the Pythagorean theorem, yielding

magnitude: Sqrt(X² + Y²) = Sqrt(22.42² + 132.42²) = 134.31 m

Direction: tan⁻¹(Y/X) = tan⁻¹(132.42/22.42) = 80.4 deg north of east

4 0

6 days ago

A pressure cooker is a pot whose lid can be tightly sealed to prevent gas from entering or escaping. even without knowing how bi

Sav [1095]

Even if we lack details about the size of the pressure cooker or the altitude of its operation, we can reliably assess the force on the lid based on prior knowledge because, similar to boiling water, the pressure buildup inside the cooker increases in line with the rising temperature.

5 0

2 days ago