1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
A slender rod is 80.0 cm long and has mass 0.120 kg. A small 0.0200-kg sphere is welded to one end of the rod, and a small 0.050
BartSMP [9]

Answer:

Explanation:

Given that,

Slender rod

Length of rod=80cm=0.8m

Mass of slender rod=0.12kg

Sphere Bob at one end

Mass M1=0.02kg

Sphere Bod at the other end

Mass M2 =0.05kg

Linear speed of mass 2 at the lowest point

We need to calculate the change in potential of the complete system. m2 and m3 are the masses at the rod ends. note the rod centre of mass neither gains nor loses potential.

So, at the lowest point,

∆U = M2•g•y2 + M1•g•y1

Note, at the lowest point, the mass 1 is 40cm (0.4m) form the midpoint, Also, the mass 2 is -40cm(-04m) from the midpoint

∆U = M2•g•y2 + M1•g•y1

∆U=0.05•9.81•(-0.4) + 0.02•9.82•0.4

∆U=-0.1962+0.07848

∆U=-0.11772 Nm

Now, the moment of inertia of the rod is given as

I=∫r²dm

dm=2pdr

I= 2p∫r²dr

I= 2 × 0.12/0.8 ∫r²dr; from r=0 to 0.4

I=0.3 [r³/3] from r=0 to 0.4

I= 0.3 [ 0.4³/3 -0] ,from r=0 to 0.4

I=0.3 × 0.02133

I=0.0064kg/m².

calculating of inertia of the end masses.

I(1+2)=Σmr² = (m1+m2)r²

I(1+2)=(0.02+0.05)0.4²

I(1+2)=0.07×0.4²

I(1+2)=0.0112 kg/m²

Now, the Energy of the masses due to angular velocity is given as

K.E=½ (I + I(1+2))w²

K.E=½(0.0064+0.0112)w²

K.E= 0.0088w²

Using conservation of energy

The potential energy is equal to the kinetic energy of the system

K.E=P.E

0.0088w²=0.11772

Then, w²=0.11772/0.0088

w²=13.377

w=√13.377

w=3.66rad/s

Then, the relationship between linear velocity and angular velocity is given by

v=wr

v=3.66×0.4

v=1.463m/s

The required linear speed is 1.46m/s approximately

8 0
3 years ago
Suppose a 49-N sled is resting on packed snow. The coefficient of kinetic friction is 0.11. If a person weighing 585 N sits on t
Andre45 [30]

Answer:

69.74 N

Explanation:

We are given that

Weight of sled=49 N

Coefficient of kinetic friction,\mu_k=0.11

Weight of person=585 N

Total weight==mg=49+585=634 N

We know that

Force needed to pull the sled across the snow at constant speed,F=Kinetic friction

F=\mu_k N

Where N= Normal=mg

F=0.11\times 634=69.74 N

Hence, the force is needed  to pull the sled across the snow at constant speed=69.74 N

7 0
3 years ago
How to light prodeced by nature
frutty [35]
Natural sources of light include our sun and other stars, where the source of energy is nuclear energy (recall that the moon does not produce light but merely reflects sunlight), lightning, where the source is electrical, and fire, where the energy source is chemical.
4 0
3 years ago
Ahmad is riding his bicycle. He finds that he can accelerate from rest at 0.44 m/s^2 for 5 s to reach a speed of 2.2 m/s. The to
snow_lady [41]

Answer:

1) The force Christian can exert on his bicycle before picking up the the cargo is 529.74 N

2) The force Christian can exert on his bicycle after picking up the the cargo is 647.46 N

Therefore, Christian has to exert more force on his bike after picking up the cargo

Explanation:

The given parameters are;

The mass of Christian and his bicycle = 54 kg

The mass of the cargo = 12 kg

1) The force Christian can exert on his bicycle before picking up the the cargo = Mass of Christian and his bicycle × Acceleration due to gravity

∴ The force Christian can exert on his bicycle before picking up the the cargo = 54 kg × 9.81 m/s² = 529.74 N

2) The force Christian can exert on his bicycle after picking up the the cargo = (54 + 12) kg × 9.81 m/s² = 647.46 N

Therefore, Christian has to exert more force on his bike after picking up the cargo.

7 0
3 years ago
Write short letters.
Svetradugi [14.3K]

Answer:

No. 67

Peter Street

12th Road

Chennai

24th June 201_

Dear Amrish

I have come to know that since your school has closed for the Autumn Break you have plenty of free time at your disposal at the moment. I would like to tell you that even I am having holidays now.

It has been a long time since we have spent some time together. If you are free, I would welcome to have your company this weekend. Why don’t you come over to my house and spend a day or so with me?

I am anxiously waiting for your reply.

Yours affectionately

your name

4 0
3 years ago
Read 2 more answers
Other questions:
  • What happens to hydrogen in the core of stars
    14·1 answer
  • Why are pots and pans made of metals like steel and their handles made of plastic?
    8·1 answer
  • A strand of 10 lights is plugged into an outlet. How can you determine if the lights are connected in series or parallel? Select
    8·1 answer
  • Are the Sun's rays like mechanical or electromagnetic waves
    8·2 answers
  • Which of the following statements concerning the electric field inside a conductor is true?
    8·1 answer
  • Party hearing. As the number of people at a party increases, you must raise your voice for a listener to hear you against the ba
    14·1 answer
  • The moon sun is directly overhead at the equator during ( a solstice or an equinox)?.
    9·1 answer
  • During World War I, the Germans had a gun called Big Bertha that was used to shell Paris. The shell had an initial speed of 0.88
    9·1 answer
  • If a special type of ice has a specific heat capacity of 2060 J/kg K. How
    15·1 answer
  • The displacement x with respect to time t of a particle moving in simple harmonic motion is given by x = 5cos(16pi*t). where x i
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!