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3 years ago

If a set of displacement vectors laid head to tail make a closed polygon, what is the resultant vector?

Physics

1 answer:

Papessa [141]3 years ago

4 0

The resultant vector is zero.

Explanation:

When you add displacement vectors using the head to tail method, you follow this procedure:

- Draw the first vector

- Draw the second vector, with its tail starting from the head of the first vector

- Draw the third vector, with its tail starting from the head of the second vector

.. and so on.

The resultant of the all vectors will be the vector connecting the tail of the 1st vector to the head of the last vector.

In this problem, the vectors make a closed polygon: this means that the head of the last vector coincides with the tail of the first vector.

Therefore, this means that the length of the resultant vector is zero.

Learn more about vector addition:

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A group of hikers hear an echo 3.3 s after they shout. The temperature is 20◦C.

romanna [79]

Answer:

560 m

Explanation:

The speed of sound in air is approximately:

v ≈ v₀ + 0.6T

where v₀ is the speed of sound at 0°C (273 K) in m/s, and T is the temperature in Celsius.

The speed of sound at 20°C at that altitude is:

v ≈ 327 + 0.6(20)

v ≈ 339 m/s

The sound travels from the hikers to the mountain and back again, so it travels twice the distance.

339 m/s = 2d / 3.3 s

2d = 1118.7 m

d = 559.35 m

Rounding, the mountain is approximately 560 m away.

4 0

3 years ago

Q1 is located at the origin, Q2 is located at x = 2.50 cm and Q3 is located at x = 3.50 cm. Q1 has a charge of +4.92μC and Q3 ha

Inessa05 [86]

Answer:

$+1.11\mu C$

Explanation:

A charge located at a point will experience a zero electrostatic force if the resultant electric field on it due to any other charge(s) is zero.

$Q_1$ is located at the origin. The net force on it will only be zero if the resultant electric field intensity due to $Q_2$ and $Q_3$ at the origin is equal to zero. Therefore we can perform this solution without necessarily needing the value of $Q_1$ .

Let the electric field intensity due to $Q_2$ be + $E_2$ and that due to $Q_3$ be - $E_3$ since the charge is negative. Hence at the origin;

$+E_2-E_3=0..................(1)$

From equation (1) above, we obtain the following;

$E_2=E_3.................(2)$

From Coulomb's law the following relationship holds;

$+E_2=\frac{kQ_2}{r_2^2}\\$

$-E_3=\frac{kQ_3}{r_3^2}$

where $r_2$ is the distance of $Q_2$ from the origin, $r_3$ is the distance of $Q_3$ from the origin and k is the electrostatic constant.

It therefore means that from equation (2) we can write the following;

$\frac{kQ_2}{r_2^2}=\frac{kQ_3}{r_3^2}.................(3)$

k can cancel out from both side of equation (3), so that we finally obtain the following;

$\frac{Q_2}{r_2^2}=\frac{Q_3}{r_3^2}................(4)$

Given;

$Q_2=?\\r_2=2.5cm=0.025m\\Q_3=-2.18\mu C=-2.18* 10^{-6}C\\r_3=3.5cm=0.035m$

Substituting these values into equation (4); we obtain the following;

$\frac{Q_2}{0.025^2}=\frac{2.18*10^{-6}}{0.035^2}\\\\hence;\\\\Q_2=\frac{0.025^2*2.18*10^{-6}}{0.035^2}\\$

$Q_2=\frac{0.00136*10^{-6}}{0.00123}=1.11*10^{-6}C\\\\Q_3=+1.11\mu C$

6 0

3 years ago

Which of the following is a false statement? Select one:

Art [367]

Answer:

The false statement is in option 'd': The center of mass of an object must lie within the object.

Explanation:

Center of mass is a theoretical point in a system of particles where the whole mass of the system is assumed to be concentrated.

Mathematically the position vector of center of mass is defined as

$\overrightarrow{r}_{com}=\int \overrightarrow{r}_{i}dm$

where,

$\overrightarrow{r}_{i}$ is the position vector of the mass dm.

As we can see for homogenous symmetrical objects such as a sphere,cube,disc the center of mass is located at the centroid of the shapes itself but in many shapes it is located outside the body also.

Examples of shapes in which center of mass is located outside the body:

1) Horseshoe shaped body.

2) A thin ring.

In many cases we can make shapes of bodies whose center of mass lies outside the body.

6 0

3 years ago

What is the magnitude of velocity for a 2000 kg car possessing 3000 kgm/s of momentum

Alex

For this case we have that by definition, the momentum is given by:

$p = mv$