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musickatia [10]
2 years ago
12

A uniform stationary ladder of length L = 4.5 m and mass M = 11 kg leans against a smooth vertical wall, while its bottom legs r

est on a rough horizontal floor. The coefficient of static friction between floor and ladder is μ = 0.49. The ladder makes an angle θ = 54° with respect to the floor. A painter of mass 8M stands on the ladder a distance d from its base.
a. Find an expression for the magnitude of the normal force N exerted by the floor on the ladder.
b. Find an expression for the magnitude of the normal force NW exerted by the wall on the ladder.
c. Find an expression for the largest value of dmax for which the ladder does not slip.
d. What is the largest value for d, in centimeters, such that the ladder will not slip? Assume that ladder is 4.5 m long, the coefficient of friction is 0.59, the ladder is at an angle of 43.5°, and the ladder has a mass of 55 kg.
Physics
1 answer:
Ostrovityanka [42]2 years ago
3 0

Answer:

a)  N = 9 Mg

, b)N_w =  μ 9M

, c)  

Explanation:

a) For this part we write the equations of trslacinal equilibrium

Axis y

       N - Mg - 8M g = 0

       N = 9 Mg

        N = 9 11 9.8

        N = 970.2 N

b) the force on the horizontal axis (x) som

        fr -N_w = 0

        fr = N_w

friction force is

       fr = μ N

      N_w =  μ 9M

g

      fr = 0.59 970.2

      fr = N_w = 572,418 N

c) For this part we must use rotational equilibrium.

         Στ = 0

We set a frame of reference at the bottom of the ladder and assume that the counterclockwise acceleration is positive

the weight of it is at its midpoint (L / 2)

      - W L /2 cos 54 - 8M d_max cos 54+ NW L sin 54 = 0

        8M d_max cos 54 = - W L / 2 cos 54 + NW L sin 54

       d_max = L (-Mg 1/2 cos 54 + NW sin 54) / (8M cos 54)

       d_max = L (-g / 16 + μ 9Mg / 8M tan 54)

       d_max = L ( 9/8 μ g tan 54- g/16)

   

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Answer:

<em>b. The current in the loop always flows in a counterclockwise direction.</em>

<em></em>

Explanation:

When a magnet falls through a loop of wire, it induces an induced current on the loop of wire. This induced current is due to the motion of the magnet through the loop, which cause a change in the flux linkage of the magnet. According to Lenz law, the induced current acts in such a way as to repel the force or action that produces it. For this magnet, the only opposition possible is to stop its fall by inducing a like pole on the wire loop to repel its motion down. An induced current that flows counterclockwise in the wire loop has a polarity that is equivalent to a north pole on a magnet, and this will try to repel the motion of the magnet through the coil. Also, when the magnet goes pass the wire loop, this induced north pole will try to attract the south end of the magnet, all in a bid to stop its motion downwards.

3 0
2 years ago
In a jump spike, a volleyball player slams the ball from overhead and toward the opposite floor. controlling the angle of the sp
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V ( initial ) = 20 m/s
h = 2.30 m
h = v y * t + g t ² / 2
d = v x * t
1 ) At α = 18°:
v y = 20 * sin 18° = 6.18 m/s
v x = 20 * cos 18° = 19.02 m/ s
2.30 = 6.18 t + 4.9 t²
4.9 t² + 6.18 t - 2.30 = 0
After solving the quadratic equation ( a = 4.9, b = 6.18, c = - 2.3 ):
t 1/2 = (- 6.18 +/- √( 6.18² - 4 * 4.9 * (-2.3)) ) / ( 2 * 4.9 )  
t = 0.3 s
d 1 = 19.02 m/s * 0.3 s = 5.706 m
2 ) At  α = 8°:
v y = 20* sin 8° = 2.78 m/s
v x = 20* cos 8° = 19.81 m/s
2.3 = 2.78 t + 4.9 t² 
4.9 t² + 2.78 t - 2.3 = 0
t = 0.46 s
d 2 = 19.81 * 0.46 = 9.113 m
The distance is:
d 2 - d 1 = 9.113 m - 5.706 m = 3.407 m

GOOD LUCK AND HOPE IT HELPS U
6 0
2 years ago
In a house the temperature at the surface of a window is 28.9 °C. The temperature outside at the window surface is 7.89 °C. Heat
Alenkasestr [34]

Answer:

-13.18°C

Explanation:

To develop the problem it is necessary to consider the concepts related to the thermal conduction rate.

Its definition is given by the function

\frac{Q}{t} = \frac{kA\Delta T}{d}

Where,

Q = The amount of heat transferred

t = time

k = Thermal conductivity constant

A = Cross-sectional area

\Delta T = The difference in temperature between one side of the material and the other

d= thickness of the material

The problem says that there is a loss of heat twice that of the initial state, that is

Q_2 = 2*Q_1

Replacing,

kA\frac{\Delta T_m}{x} = 2*kA\frac{\Delta T}{x}

\frac{\Delta T}{x}=2*\frac{\Delta T}{x}

\frac{T_i-T_o}{x} = 2\frac{T_1-T_2}{x}

\frac{28.9-T_o}{x} = 2\frac{28.9-7.86}{x}

Solvinf for T_o,

T_o = -13.18

Therefore the temprature at the outside windows furface when the heat lost per second doubles is  -13.18°C

3 0
2 years ago
A professor's office door is 0.99 m wide, 2.2 m high, 4.2 cm thick; has a mass of 27 kg, and pivots on frictionless hinges. A "d
ANEK [815]

Answer:

I=8.8209\ kg.m^2

\alpha=0.6348\ rad.s^{-2}

Explanation:

Given:

  • width of door, w=0.99\ m
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  • thickness of the door, t=4.2\ cm
  • mass of the door, m=27\ kg
  • torque on the door, \tau=5.6\ N.m

<em>∵Since the thickness of the door is very less as compared to its other dimensions, therefore we treat it as a rectangular sheet.</em>

  • For a rectangular sheet we have the mass moment of inertia inertia as:

I=\frac{1}{3} m.w^2

I=\frac{1}{3}\times 27\times 0.99^2

I=8.8209\ kg.m^2

We have a relation between mass moment of inertia, torque and angular acceleration as:

\alpha=\frac{\tau}{I}

\alpha=\frac{5.6}{8.8209}

\alpha=0.6348\ rad.s^{-2}

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2 years ago
2. Harry is pushing a car down a level road at 2.0 m/s with a force of 243 N. The total force
Arte-miy333 [17]

b) Equal to 243 N.

Explanation:

The total force acting on the car in the opposite direction including the road friction and air resistance is equal to 243 N.

This is in conformity with newton's third law of motion.

Newton's third law of motion states that "action and reaction are equal and opposite in direction. "

  • The action force is that of the pull by Harry acting on the car.
  • The reaction force is in the opposite direction.
  • Both action and reaction force equal and opposite and magnitude and direction

learn more:

Newton's laws brainly.com/question/11411375

#learnwithBrainly

3 0
2 years ago
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