By counting the number of crests that pass in a given amount of time, a person can calculate the

One end of a string is fixed. An object attached to the other end moves on a horizontal plane with uniform circular motion of ra

sveticcg [70]

Answer:

If both the radius and frequency are doubled, then the tension is increased 8 times.

Explanation:

The radial acceleration ( $a_{r}$ ), measured in meters per square second, experimented by the moving end of the string is determined by the following kinematic formula:

$a_{r} = 4\pi^{2}\cdot f^{2}\cdot R$ (1)

Where:

$f$ - Frequency, measured in hertz.

$R$ - Radius of rotation, measured in meters.

From Second Newton's Law, the centripetal acceleration is due to the existence of tension ( $T$ ), measured in newtons, through the string, then we derive the following model:

$\Sigma F = T = m\cdot a_{r}$ (2)

Where $m$ is the mass of the object, measured in kilograms.

By applying (1) in (2), we have the following formula:

$T = 4\pi^{2}\cdot m\cdot f^{2}\cdot R$ (3)

From where we conclude that tension is directly proportional to the radius and the square of frequency. Then, if radius and frequency are doubled, then the ratio between tensions is:

$\frac{T_{2}}{T_{1}} = \left(\frac{f_{2}}{f_{1}} \right)^{2}\cdot \left(\frac{R_{2}}{R_{1}} \right)$ (4)

$\frac{T_{2}}{T_{1}} = 4\cdot 2$

$\frac{T_{2}}{T_{1}} = 8$

If both the radius and frequency are doubled, then the tension is increased 8 times.

5 0

2 years ago

A father is pulling his child on a sled in the snow. According to Newton’s Third Law, the force the father exerts on the sled is

viktelen [127]

That is because there are other forces like the friction forces that apply differently on both of them. The frictional forces applied to the sled are smaller than they are on the father, for example, so it's possible for him to pull it.

5 0

3 years ago

Suppose Mary would like to design an emergency overheating alarm using one of these materials. In her design, at room temperatur

Reptile [31]

Answer:

A. 92.88 °C

B. 401.535 °C

Explanation:

So, the overheating system is going to be based on the principle of thermal linear expansion. The behavior of this principle is ruled by the equation:

∆L= L_i * ∆T * α

Where α is a coefficient of linear expansion. For a cylinder made from polycarbonate α = 70,2*10^(-6) °C^(-1) and for a cylinder made from cast iron α = 12*10^(-6) °C^(-1). If we isolate the term of the temperature’s difference, we have:

∆L/(L_i * α) = ∆T → T_f = T_i + ∆L/(L_i * α)

Replacing the values, for the case of the Polycarbonate we have:

T_f = T_i + ∆L/(L_i * α) = 23°C+0,0273cm/(6,01cm *70,2 * 10^(-6)°C^(-1) ) = 92,88 °C

Replacing the values, for the case of the Cast Iron we have:

T_f = T_i +∆L/(L_i * α) = 23°C + 0,0273cm/(6,01cm * 12 * 10^(-6) °C^(-1) ) = 401,535 °C

As we see, is way better to use the polycarbonate in this application.

Have a nice day. Let me know if I can help you with anything else. :D

4 0

2 years ago

Four point charges are placed at the corners of a square. Each charge has the identical value +Q. The length of the diagonal of

kvv77 [185]

Answer: $V_{net}=4\frac{kQ}{a}$