What are elements made up of? atoms matter Hydrogen substance

A 0.26 kg rod of length 80 cm is suspended by a frictionless pivot at one end. It is held horizontal and released.

Daniel [21]

Answer:

a) $a_{center} = 7.38 ~m/s^2$

b) $a_{end} = 14.77 ~m/s^2$

c) $v_{center} = 2.43~m/s$

Explanation:

a) Immediately after the rod is released, the rod is still horizontal but now subject to gravity. Since one end of the rod is fixed, then the weight of the rod applies a torque. Then by Newton's Second Law, the acceleration can be found.

$\tau =I\alpha$

where I is the moment of inertia of the rod with respect to its fixed end, and α is the angular acceleration.

The net torque of the rod is

$\vec{\tau} = \vec{r} \times \vec{F}\\\tau = rF\sin(90) = rF$

where r is the distance from center of the mass to the fixed end, so r = 0.4 m.

The weight of the rod is w = mg = 0.26 x 9.8 = 2.54 N.

So the net torque is τ = 1.01 Nm.

The moment of inertia of the rod is

$I = \frac{1}{3}mL^2 = \frac{1}{3}(0.26)(0.8)^2 = 0.055~kg m^2$

So, the Newton's Second Law yields

$\tau = I\alpha\\\alpha = \frac{\tau}{I} = \frac{1.01}{0.055} = 18.47$

The relation between angular acceleration and linear acceleration is a = αr

So, the linear acceleration of the rod is

$a = \alpha r = 7.38~m/s^2$

b) Using the same relationship between angular acceleration and linear acceleration, the linear acceleration of the end of the rod can be found.

$a = \alpha L = 14.77~m/s^2$

c) The conservation of energy can be used to find the velocity when the rod is vertical.

$K_1 + U_1 = K_2 + U_2\\0 + mg(L/2) = \frac{1}{2}I\omega^2 + 0\\(0.26)(9.8)(0.4) = \frac{1}{2}(0.055)\omega^2\\\omega = 6.08~rad/s$

The linear velocity is v = ωr, so

v = 2.43 m/s.

4 0

3 years ago

Which structures allow for the removal of wastes from the developing fetus?

castortr0y [4]

The fetus relies upon its mother as it develops. These are some of the things it needs:

protection against knock and bumps, and temperature changes oxygen for respiration nutrients (food and water)

The developing fetus also needs its waste substances removing.

The fetus is protected by the uterus and the amniotic fluid, a liquid contained in a bag called the amnion.

5 0

4 years ago

A fugitive tries to hop on a freight train traveling at a constant speed of 5.5 m/s. Just as an empty box car passes him, the fu

stiks02 [169]

Th equations to be used here are the following:

a = (v - v₀)/t
x = v₀t + 0.5at²

The speed of the fugitive is the sum of his own speed plus the speed of the train. Thus,
v₀ = 0 + 5.5 m/s = 5.5 m/s
v = 8 m/s + 5.5 m/s = 13.5 m/s

a.) We use the first equation to determine time
2.5 m/s² = (13.5 m/s - 5.5 m/s)t
Solving for t,
t = 3.2 seconds

b.) We use the answer in a) and the 2nd equation:

x = (5.5 m/s)(3.2 s) + 0.5(2.5 m/s²)(3.2 s)²
x = 30.4 meters

3 0

3 years ago

4. Friction is required for :

Aneli [31]

Both of the above! :)

5 0

3 years ago

Read 2 more answers

What is an inertial reference frame?

Gennadij [26K]

<h2>Answer: A system in which Newton's Laws are fulfilled</h2>

An inertial reference system is a reference system in which the principle of inertia is fulfilled, which is one of Newton's laws:

"For a body to have acceleration, an external force must act on it"

In addition, the other Newton's laws of movement are fulfilled.

Therefore, the variation of the linear momentum of the system is equal to the actual forces on the system.

8 0

3 years ago