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creativ13 [48]
3 years ago
9

A rope of negligible mass passes over a uniform cylindrical pulley of 1.50 kg mass and 0.090 m radius. The bearings of the pulle

y have negligible friction, and the rope does not slip on the pulley. On one end of the rope hangs a 3.00 kg bunch of bananas, and on the other end hangs a 4.50 kg monkey. Calculate the downward acceleration of the monkey and the tension in both ends of the rope.

Physics
1 answer:
madreJ [45]3 years ago
7 0

Answer:

1.8 m/s²

36 N

34.8 N

Explanation:

For the monkey :

m₁ = mass of monkey = 4.50 kg

T₁ = Tension force in the rope on monkey's side

a = acceleration

From the force diagram, force equation for the motion of monkey is given as

m₁ g - T₁ = m₁ a

(4.50 x 9.8) - T₁ = 4.5 a

T₁ = 44.1 - 4.5 a                                             eq-1

For the bunch of bananas :

m₂ = mass of bunch of bananas = 3 kg

T₂ = tension force in the rope on the side of banana

From the force diagram, force equation for the motion of bananas is given as

T₂ - m₂ g = m₂ a

T₂ - (3 x 9.8) = 3 a

T₂ = 29.4 + 3 a                                            eq-2

m = mass of the pulley = 1.50 kg

r = radius of the pulley = 0.090 m

α = angular acceleration of pulley = a/r

Torque equation for the pulley is given as

(T₁ - T₂ )r = I α

(T₁ - T₂ )r = I (a/r)

T₁ - T₂  = (0.5 m r²) (a/r²)

T₁ - T₂  = (0.5) ma

using eq-1 and eq-2

44.1 - 4.5 a  - (29.4 + 3 a) = (0.5) ma

44.1 - 4.5 a  - (29.4 + 3 a) = (0.5) (1.50) a

a = 1.8 m/s²

Using eq-1

T₁ = 44.1 - 4.5 a    

T₁ = 44.1 - 4.5 (1.8)    

T₁ = 36 N

using eq-2

T₂ = 29.4 + 3 a

T₂ = 29.4 + 3 (1.8)

T₂ = 34.8 N

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What displacement in cm would occur with a 75 N/m spring if you placed a 300 N weight on the spring?
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Surface tension=75N/m

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\\ \bull\tt\longmapsto Surface\:Tension=\dfrac{Weight}{Displacement}

\\ \bull\tt\longmapsto Displacement=\dfrac{Weight}{Surface\:Tension}

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\\ \bull\tt\longmapsto Displacement=4m

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During a workout, the football players at State U ran up the stadium stairs in 61 s. The stairs are 130 m long and inclined at a
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Answer:

  P = 1097 Watt

Explanation:

given,

length of stairs, L = 130 m

inclination with horizontal,θ = 30°

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time = 61 s

we know,

Power = \dfrac{work}{time}

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Explain how microorganisms are friend and foe.​
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2. A student drives 7.8-km trip to school and averages a speed of
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<em>The total time is: t=451.22 sec</em>

<em>The average speed is: V=34.57 m/s</em>

Explanation:

<u>Average speed</u>

The average speed is calculated by dividing the total distance traveled by an object (x) by the total time it took it to travel that distance (t).

\displaystyle V=\frac{x}{t}

Since the student makes the trip in two parts, we have to calculate the total distance and the total time.

We know the distance to school is 7.8 Km = 7,800 m. The student makes his way home over the same distance, thus the total distance is

x=2*7,800 m=15,600 m

The first trip to school was done at an average speed of v1=32.6 m/s. Knowing the distance and speed, we can calculate the time:

\displaystyle t1=\frac{x1}{v1}=\frac{7,800}{32.6}=239.26\ sec

The second trip back home was done at an average speed of v2=36.8 m/s. Let's calculate the second time:

\displaystyle t2=\frac{x2}{v2}=\frac{7,800}{36.8}=211.96\ sec

The total time is:

t=239.26\ sec+211.96\ sec=451.22\ sec

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\displaystyle V=\frac{15,600}{451.22}=34.57\ m/s

\boxed{\displaystyle V=34.57\ m/s}

6 0
3 years ago
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