Pls help me... taking a quiz.

Force F → = (−8.0 N)iˆ + (6.0 N)jˆ acts on a particle with position vector r → = (3.0 m)iˆ + (4.0 m)jˆ. What are (a) the torque

disa [49]

Answer with Explanation:

We are given that

$F=-8\hat{i}+6\hat{j}$

$r=3\hat{i}+4\hat{j}$

a.We have to find the torque on the particle about the origin.

We know that

Torque= $\tau=r\times F=\begin{vmatrix}i&j&k\\3&4&0\\-8&6&0\end{vmatrix}$

By using the formula

$\tau=50\hat{k}$

b. $\mid \tau\mid =\mid F\mid \mid r\mid sin\theta$

$\mid F\mid=\sqrt{(-8)^2+(6)^2}=10$

$\mid r\mid=\sqrt{3^2+4^2}=5$

$\mid \tau\mid=\sqrt{(-50)^2}=50$

Substitute the values then we get

$50=10\times 5 sin\theta$

$sin\theta=\frac{50}{50}=1$

$sin\theta=sin90^{\circ}$

Because $sin90^{\circ}=1$

$\theta=90^{\circ}$

3 0

3 years ago

The acceleration due to gravity, g , is constant at sea level on the Earth's surface. However, the acceleration decreases as an

blsea [12.9K]

Answer:

g = g₀ [1- 2 h / Re + 3 (h / Re)²]

Explanation:

The law of universal gravitation is

F = G m Me / Re²

Where g is the universal gravitational constant, m and Me are the mass of the body and the Earth, respectively and R is the distance between them

F = G Me /Re² m

We call gravity acceleration a

g₀ = G Me / Re².

When the body is at a height h above the surface the distance is

R = Re + h

Therefore the attractive force is

F = G Me m / (Re + h)²

Let's take Re's common factor

F = G Me / Re² m / (1+ h / Re)²

As Re has a value of 6.37 10⁶ m and the height of the body in general is less than 10⁴ m, the h / Re term is very small, so we can perform a series expansion

(1+ h / Re)⁻² = 1 -2 h / Re + 6/2 (h / Re) 2 + ...

Let's replace

F = G Me /Re² m [1- 2 h / Re + 3 (h / Re)²]

F = g₀ m [1- 2 h / Re + 3 (h / Re)²]

If we call the force of attraction at height

m g =g₀ m [1- 2 h / Re + 3 (h / Re)²]

g = g₀ [1- 2 h / Re + 3 (h / Re)²]

3 0

3 years ago

An object is located 10.0 cm from a convex mirror. The magnitude of the

Sunny_sXe [5.5K]

Answer:

B. 6.00 cm

Explanation:

6 0

3 years ago

A block is attached to the end of a horizontal ideal spring and rests on a frictionless surface. The block is pulled so that the

bezimeni [28]

Answer:

The answer is "a, c and b"

Explanation:

Its total block power is equal to the amount of potential energy and kinetic energy.
Because the original block expansion in all situations will be the same, its potential power in all cases is the same.
Because the block in the first case has no initial speed, the block has zero film energy.
For both the second example, it also has the $v_o$ velocity, but the kinetic energy is higher among the three because its potential and kinetic energy are higher.
While over the last case the kinetic speed is greater and lower than in the first case, the total energy is also higher than the first lower than that of the second.
The greater the amplitude was its greater the total energy, therefore lower the second, during the first case the higher the amplitude.

4 0

2 years ago

Why is random sampling and random assignment in experimental research important?

Hunter-Best [27]

So the result is not biased or affected in some way

6 0

3 years ago