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Anestetic [448]
3 years ago
7

A firefighter with a weight of 707 N slides down a vertical pole with an acceleration of 2.79 m/s2, directed downward. (a) What

is the magnitude of the vertical force on the firefighter from the pole?
Physics
1 answer:
DedPeter [7]3 years ago
7 0

Answer:

The vertical force acting on the firefighter = 908.27 N

Explanation:

Force: Force of a body is defined as the product of mass and its acceleration. The S.I unit of force is Newton (N)

The vertical force acting on the firefighter = Force due to the weight of the firefighter + force due to acceleration.

Ft = Fw - Fa

Where Ft = The vertical force acting on the firefighter, Fw = Force due to the weight of the firefighter, Fa = force due to acceleration.

Fw = mg

Making m the subject of formula in the equation above

m = Fw/g................... Equation 1

Where m = mass of the firefighter, g = acceleration due to gravity,

<em>Given: Fw = 707 N, </em>

<em> Constant: g = 9.8 m/s²</em>

Substituting these values into eqaution 1

m = 707/9.8

m = 72.14 kg.

But, Fa = ma

Where a = acceleration of the firefighter.

<em>Given: a = 2.79 m/s², </em>

<em>And m = 72.14 kg</em>

Fa = 72.14 × 2.79

Fa = 201.27 N

Therefore, Ft = 707 + 201.27  = 908.27 N

Ft = 908.27 N

The vertical force acting on the firefighter = 908.27 N

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A hollow cylinder with an inner radius of 5 mm and an outer radius of 26 mm conducts a 4-A current flowing parallel to the axis
bearhunter [10]

Answer:

B = 38.2μT

Explanation:

By the Ampere's law you have that the magnetic field generated by a current, in a wire, is given by:

B=\frac{\mu_o I_r}{2\pi r}     (1)

μo: magnetic permeability of vacuum = 4π*10^-7 T/A

r: distance from the center of the cylinder, in which B is calculated

Ir: current for the distance r

In this case, you first calculate the current Ir, by using the following relation:

I_r=JA_r

J: current density

Ar: cross sectional area for r in the hollow cylinder

Ar is given by  A_r=\pi(r^2-R_1^2)

The current density is given by the total area and the total current:

J=\frac{I_T}{A_T}=\frac{I_T}{\pi(R_2^2-R_1^2)}

R2: outer radius = 26mm = 26*10^-3 m

R1: inner radius = 5 mm = 5*10^-3 m

IT: total current  = 4 A

Then, the current in the wire for a distance r is:

I_r=JA_r=\frac{I_T}{\pi(R_2^2-R_1^2)}\pi(r^2-R_1^2)\\\\I_r=I_T\frac{r^2-R_1^2}{R_2^2-R_1^2}  (2)

You replace the last result of equation (2) into the equation (1):

B=\frac{\mu_oI_T}{2\pi r}(\frac{r^2-R_1^2}{R_2^2-R_1^2})

Finally. you replace the values of all parameters:

B=\frac{(4\pi*10^{-7}T/A)(4A)}{2\PI (12*10^{-3}m)}(\frac{(12*10^{-3})^2-(5*10^{-3}m)^2}{(26*10^{-3}m)^2-(5*10^{-3}m)^2})\\\\B=3.82*10^{-5}T=38.2\mu T

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Answer:

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Explanation:

Given that,

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Final position of the ball,  X₂ = -25 m

Time taken to travel is, t = 2.5 s

The average velocity of the ball is given by the formula,

                       V = X₂ - X₁ / t     m/s

Substituting the values in the above equation,

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                          = -14 m/s

The negative sign in the velocity indicates that ball rolls in the opposite direction.

Hence, the average velocity of the ball is  v = -14 m/s

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