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Solnce55 [7]
3 years ago
5

A free undamped spring/mass system oscillates with a period of 4 seconds. When 10 pounds are removed from the spring, the system

then has a period of 2 seconds. What was the weight of the original mass on the spring? (Round your answer to one decimal place.)
Physics
1 answer:
OverLord2011 [107]3 years ago
6 0

Answer:

13.3 pounds.

Explanation:

For a spring of constant K, with an attached object of mass M, the period can be written as:

T = 2*π*√(M/K)

Where π = 3.14

First, we know that the period is 4 seconds, then we have:

4s = (2*π)*√(M/K)

We know that if the mass is reduced by 10lb, the period becomes 2s.

Then the new mass of the object will be: (M - 10lb)

Then the period equation becomes:

2s = (2*π)*√((M-10lb)/K)

So we have two equations:

4s = (2*π)*√(M/K)

2s = (2*π)*√((M-10lb)/K)

We want to solve this for M.

First, we need to isolate K in one of the equations.

Let's isolate K in the first one:

4s = (2*π)*√(M/K)

(4s/2*π) = √(M/K)

(2s/π)^2 = M/K

K = M/(2s/π)^2 = M*(π/2s)^2

Now we can replace it in the other equation.

2s = (2*π)*√((M-10lb)/K)

First, let's simplify the equation:

2s/(2*π) = √((M-10lb)/K)

1s/π =  √((M-10lb)/K)

(1s/π)^2 =  ((M-10lb)/K

K*(1s/π)^2 = M - 10lb

Now we can use the equation: K =  M*(π/2s)^2

then we get:

K*(1s/π)^2 = M - 10lb

(M*(π/2s)^2)*(1s/π)^2 = M - 10lb

M/4 = M - 10lb

10lb = M - M/4

10lb = (3/4)*M

10lb*(4/3) = M

13.3 lb = M

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D do.

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2 years ago
An object of unknown mass is hung on the end of an unstretched spring and is released from rest. The acceleration of gravity is
lakkis [162]

Answer:

0.33 s

Explanation:

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For this system, we can determine the period of the motion using the following formula:

T = 2π√(L/g)

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By the exact time the object is 2.75 cm before coming to rest, that will be the lenght of the spring we can consider (2.75 cm = 0.0275 m)

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4 0
3 years ago
Hey, I need help with my homework.
Anna11 [10]

We have that the Average Force is given

Avg F=2.0488N

 

From the question we are told

Masses=

0.10

0.25

0.40

0.50

0.60

0.75

1

1.5

2

Accelerations

9.5

4.2

2.3

2.1

1.7

1.3

1.1

0.7

0.5

Generally the equation for the Mean is mathematically given as

For Mass

X=\frac{\sum x}{n}\\\\X=\frac{0.10 +0.25+0.40+0.50+0.60+0.75+1+1.5+2}{9}\\\\X=0.788g

For Acceleration

X'=\frac{\sum x}{n}\\\\X'=\frac{9.5+4.2+2.3+2.1+1.7+1.3+1.1+0.7+0.5}{9}\\\\X'=2.6m/s^2

Since Average Acceleration and mass are found above

Therefore

The Average Force is given as

Generally the equation for the Average Force is mathematically given as

Avg F=Avg m *Avg a\\\\Avg F=0.788*2.6\\\\Avg F=2.0488

For more information on this visit

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3 years ago
Sam is riding his bike and spots a sinkhole. He slows his bike from 14.0 m/s to 2.0 m/s on 6.0 seconds. What is the bikes negati
VARVARA [1.3K]
By definition, average acceleration will be:
a=(v(f)-v(i))/t
a=(2-14)/6=-2 (m/s^2)
________
-2(m/s^2)
4 0
3 years ago
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