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Ivahew [28]
3 years ago
9

You've always wondered about the acceleration of the elevators in the 101-story-tall Empire State Building. One day, while visit

ing New York, you take your bathroom scale into the elevator and stand on it. The scale reads 150 lb as the door closes. The reading varies between 120 lb and 170 lb as the elevator travels 101 floors.
i)What is the maximum acceleration upward?
ii)What is the maximum magnitude of the acceleration downward
Physics
1 answer:
kondor19780726 [428]3 years ago
8 0

Answer:

(i) The maximum acceleration upward is 2.02 m/s².

(ii) The maximum acceleration downward is 1.39 m/s².

Explanation:

Let a be the maximum acceleration of the elevator.

The mass of the person at ground is 150 lb. We have to convert the mass into kg,

1 lb = 0.453592 kg

150 lb = 68 kg

170 lb = 77 kg

120 lb = 54 kg

(i) The person experience a force due to Earth's gravity in the downwards direction. The magnitude of this force is:

F₁ = mg = 68 x 9.8 = 666.4 N

The weight of the person decreases as the elevator is moving upwards. So, the force experienced by the person in this case due to gravity is:

F₂ = 54 x 9.8 = 529.2 N

Applying Newton's force equation;

(F₁ - F₂) = ma

(666.4 - 529.2) = 68 x a

a = 2.02 m/s²

(ii) The weight of the person increases as the elevator is moving downwards. So, the force experienced by the person in this case due to gravity is:

F₂ = 77 x 9.8 = 754.6 N

Applying Newton's force equation;

(F₁ - F₂) = ma

(666.4 - 754.6) = 68 x a

a = -1.30 m/s²

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A box is sliding down an incline tilted at a 11.1° angle above horizontal. The box is initially sliding down the incline at a sp
raketka [301]

Answer:s=0.68 m

Explanation:

Given

Inclination \theta =11.1^{\circ}

Speed of block(u)=1.6 m/s

Coefficient of kinetic Friction \mu _k=0.39

deceleration provided by friction=g\sin \theta -\mu _kg\cos \theta [/tex]

Using v^2-u^2=2as

Final velocity v=0

0-1.6^2=2(g\sin \theta -\mu _kg\cos \theta )s

s=\frac{-1.6^2}{2\cdot (9.8\sin 11.1-0.39\times 9.8\times \cos 11.1)}

s=0.68 m

5 0
3 years ago
A playground merry-go-round of radius 2.00 m has a moment of inertia I = 275 kg · m2 and is rotating about a frictionless vertic
ryzh [129]

Answer:

0.2932 rad/s

Explanation:

r = Radius = 2 m

I_i = Initial angular momentum = 275\ kgm^2

\omega_i = Initial angular velocity = 14 rev/min

I_f = Final angular momentum

\omega_f = Final angular velocity

Here the angular momentum of the system is conserved

I_i\omega_i=I_f\omega_f\\\Rightarrow 275\times 14\times \dfrac{2\pi}{60}=(275+275(2)^2)\omega_f\\\Rightarrow \omega_f=\dfrac{275\times 14\times \dfrac{2\pi}{60}}{275+275(2)^2}\\\Rightarrow \omega_f=0.2932\ rad/s

The final angular velocity is 0.2932 rad/s

7 0
3 years ago
A coaxial cable consists of a solid inner cylindrical conductor of radius 2 mm and an outer cylindrical shell of inner radius 3
4vir4ik [10]

Answer:

d) 1.2 mT

Explanation:

Here we want to find the magnitude of the magnetic field at a distance of 2.5 mm from the axis of the coaxial cable.

First of all, we observe that:

- The internal cylindrical conductor of radius 2 mm can be treated as a conductive wire placed at the axis of the cable, since here we are analyzing the field outside the radius of the conductor. The current flowing in this conductor is

I = 15 A

- The external conductor, of radius between 3 mm and 3.5 mm, does not contribute to the field at r = 2.5 mm, since 2.5 mm is situated before the inner shell of the conductor (at 3 mm).

Therefore, the net magnetic field is just given by the internal conductor. The magnetic field produced by a wire is given by

B=\frac{\mu_0 I}{2\pi r}

where

\mu_0 is the vacuum permeability

I = 15 A is the current in the conductor

r = 2.5 mm = 0.0025 m is the distance from the axis at which we want to calculate the field

Substituting, we find:

B=\frac{(4\pi\cdot 10^{-7})(15)}{2\pi(0.0025)}=1.2\cdot 10^{-3}T = 1.2 mT

8 0
3 years ago
A proton moving at 8.00 106 m/s through a magnetic field of magnitude 1.72 T experiences a magnetic force of magnitude 7.20 10-1
gladu [14]

Answer:

19.1 deg

Explanation:

v = speed of the proton = 8 x 10⁶ m/s

B = magnitude of the magnetic field = 1.72 T

q = magnitude of charge on the proton = 1.6 x 10⁻¹⁹ C

F = magnitude of magnetic force on the proton = 7.20 x 10⁻¹³ N

θ = Angle between proton's velocity and magnetic field

magnitude of magnetic force on the proton is given as

F = q v B Sinθ

7.20 x 10⁻¹³ = (1.6 x 10⁻¹⁹) (8 x 10⁶) (1.72) Sinθ

Sinθ = 0.327

θ = 19.1 deg

4 0
3 years ago
A parachutist of mass 56.0 kg jumps out of a balloon at a height of 1400 m and lands on the ground with a speed of 5.10 m/s. How
Vlad [161]

Answer:

769,048.28Joules

Explanation:

A parachutist of mass 56.0 kg jumps out of a balloon at a height of 1400 m and lands on the ground with a speed of 5.10 m/s. How much energy was lost to air friction during this bump

The energy lost due to friction is expressed using the formula;

Energy lost  = Potential Energy + Kinetic Energy

Energy lost  = mgh + 1/2mv²

m is the mass

g is the acceleration due to gravity

h is the height

v is the speed

Substitute the given values into the formula;

Energy lost  = 56(9.8)(1400) + 1/2(56)(5.10)²

Energy lost  = 768,320 + 728.28

Energy lost  = 769,048.28Joules

<em>Hence the amount of energy that was lost to air friction during this jump is 769,048.28Joules</em>

6 0
3 years ago
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