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goblinko [34]
3 years ago
12

A particle is acted on by two torques about the origin: τ→1 has a magnitude of 8 N·m and is directed in the positive direction o

f the x axis, and τ→2 has a magnitude of 8.9 N·m and is directed in the negative direction of the y axis. In unit-vector notation, find d⁢ℓ→/d⁢t, where ℓ→ is the angular momentum of the particle about the origin.
Physics
1 answer:
lyudmila [28]3 years ago
5 0

To give solution to the exercise we must use the concepts of Torque, Vector magnitude and vector direction of the forces.

For the given problem we have to

T_i = 8Nm

T_j = -8.9Nm

In this way the torque acting on the particle as a function of distance and time is,

\tau = \frac{dL}{dt} = 8\hat{i}-8.9\hat{j}

The net torque acting on the particle is

\tau_{net} = \sqrt{T_i^2+T_j^2}

\tau_{net} = \sqrt{(8)^2+(-8.9)^2}

\tau_{net} = 11.967Nm

PART B) The direction of the torque is given by,

tan\theta = \frac{y}{x}

\theta = tan^{-1}\frac{y}{x}

\theta = tan^{-1}(\frac{-8.9}{8})

\theta = -48.04\°

Therefore the torque direction is 48.04° below the x axis.

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Your friend has been hired to design the interior of a special executive express elevator for a new office building. This elevat
Xelga [282]

Answer:

The force on each wire is  

   T_1  = 12.5 \ N

     T_2  =   25 \  N

    T_3  =  50  \  N

Explanation:

From the question we are told that

   The acceleration at which the elevator will stop is  a =  \frac{g}{4}

    The weight of each section of the wire is  W =  \ 10 \ N

Generally W_1 = W_2 = W_3 here  W_1 , W_2 , W_3 are weight at each section

Generally considering the first section, the force acting along the y-axis  is mathematically represented as

       \sum F_y_1 =  T_1 - W_1 =  m *  a

Here T_ 1 represents the tension on the wire at the first section while  W_1 represents the weight  of the lamp at the first section

So

      T_1  - 10 = m *  \frac{g}{4}

=>    T_1  - 10 =  \frac{W_1}{4}

=>    T_1  - 10 =  \frac{10}{4}

=>    T_1  = 12.5 \ N

Generally considering the second section, the force acting along the y-axis  is mathematically represented as

      \sum F_y_2 =  T_2 -T_1- W_2 =  m *  a

=>   T_2 - T_1- 10 =  m *  \frac{g}{4}

=>   T_2 - 12.5- 10 =    \frac{W_2}{4}

=>  T_2- 12.5- 10 =    \frac{10}{4}

=>   T_2  =   25 \  N

Generally considering the third  section, the force acting along the y-axis  is mathematically represented as

    \sum F_y_3 = T_3- T_2 -T_1- W_3 =  m *  a

    T_3 - T_2 - T_1- 10 =  m *  \frac{g}{4}

      T_3 - 25 - 12.5- 10 =    \frac{W_2}{4}

       T_3 - 25 - 12.5- 10 =    \frac{10}{4}

       T_3  =  50  \  N

4 0
3 years ago
A revolutionary war cannon, with a mass of 2240 kg, fires a 15.5 kg ball horizontally. The cannonball has a speed of 131 m/s aft
My name is Ann [436]

Answer:

v' = -0.0906 m/s

Explanation:

given,

mass of cannon, M = 2240 Kg

mass of the ball, m = 15.5 Kg

speed of cannon ball, v = 131 m/s

speed of he cannon = ?

initial speed of cannon and the cannon ball is equal to 0 m/s

using conservation of energy

(M+m)V = M v' + m v

(M+m) x 0= 22400 v' + 15.5 x 131

22400 v' = -2030.5

v' = -0.0906 m/s

negative sign represent the canon will move in opposite direction of the ball.

hence, speed of cannon is equal to 0.0906 m/s

8 0
3 years ago
Unweathered rock that underlies soil is subsoil. True False
Maru [420]
False.

Unweathered rock that underlies soul is known as bedrock.
5 0
3 years ago
Read 2 more answers
Two pith balls hang side by side close to each other without touching as shown in the figure below. They are both neutral to beg
Mila [183]

a)

When a plastic rod is rubbed with wool, charging by friction occurs.

This is one of the three mechanisms of charging an object: in this particular case, as the rod is rubbed with the wool, electrons jump from the wool to the rod.

As a result, the plastic rod will remain with an excess of electrons (negative charge), while the wool will remain with a lack of electrons (positive charge).

However, the number of electrons gained by the rod is equal to the number of electrons given off by the wool: therefore, the total net charge of the system rod + cloth has not changed.

b)

When the rod touches sphere A, some electrons are transferred from the rod to the sphere (this method of charging is called charging by conduction).

Then, the sphere A will also remain negatively charged, as well as the plastic rod.

Later, the rod is brought close to sphere A without touching it: here, the electrons in the rod repel the electrons in the sphere (like charges repel each other), so the rod and the sphere will repel each other.

c)

Before part b), the negative charge on the plastic rod was equal to the positive charge on the wool.

After part b), the plastic rod has given off part of its electrons to sphere A. As a result, the negative charge on the plastic rod will be now less than the positive charge on the wool.

Therefore, the net charge of the rod + wool system will now be positive.

d)

The electrostatic force between two charged object is:

- Attractive if the charges on the objects have opposite sign

- Repulsive if the charges on the objects have same sign

Since sphere A is charged negatively, when it is brought close to sphere B, the electrons in sphere B will be attracted on the opposite side relative to sphere A, while the positive charges will migrate close to sphere A. Therefore, the two spheres will attract each other, since opposite charges attract each other.

e)

When the plastic rod (which is negatively charged) touches sphere B, some electrons are transferred to sphere B (charging by induction). As a result, charge B will also be negatively charged now, as it has an excess of electrons.

At the same time, sphere A is also negatively charged. Therefore, as like charges repel each other, this means that the two spheres will now repel each other.

f)

The net charge of the rod and the two spheres is negative.

In fact, the electrons given off by the rod to the two spheres were initially on the rod itself: this means that the total net charge of the rod + 2 spheres is equal to the net charge on the rod before the process.

Since the net charge on the rod before the process was negative, then the net charge of the system consisting of the rod + 2 spheres must be negative as well.

g)

When a glass rod is rubbed with silk, charging by friction occurs, similar to part a). However in this case, the glass rod gives off electrons to the silk: therefore, the glass rod remains positively charged.

Later, the glass rod touches sphere B: as a result, positive charge is transferred from the rod to sphere B, so sphere B will remain positively charged.

In the meantime, sphere A is negatively charged: since opposite charges attract each other, this means that now sphere A and sphere B will attract each other.

h)

When the two spheres are moved a bit further apart, the attractive force between them decreases a bit. In fact, the electrostatic force between two charged objects is given by

F=k\frac{q_1 q_2}{r^2}

where

k is the Coulomb's constant

q1, q2 are the  charges on the two objects

r is the separation between the objects

As we can see, the force is inversely proportional to the square of the distance: therefore, if the separation between the spheres increases, the force will decrease.

4 0
2 years ago
Energy can be changed from one form to another. Which terms can be used to describe these changes? Check all
Ne4ueva [31]

Answer:

the answer is Energy conversion

Explanation:

I hope this helped

7 0
2 years ago
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