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
Mekhanik [1.2K]
2 years ago
10

A block of unknown mass is attached to a spring with a spring constant of 7.00 N/m 2 and undergoes simple harmonic motion with a

n amplitude of 12.5 cm. When the block is halfway between its equilibrium position and the end point, its speed is measured to be 32.0 cm/s (a )Calculate the mass of the block.
( b)Calculate the period of the motion.
(c ) Calculate the maximum acceleration of the block.
Physics
1 answer:
KatRina [158]2 years ago
5 0

Answers:

a) 0.80 kg

b) 2.12 s

c) 1.093 m/s^{2}

Explanation:

We have the following data:

k=7 N/m is the spring constant

A=12.5 cm \frac{1 m}{100 cm}=0.125 m is the amplitude of oscillation

V=32 cm/s=0.32 m/s is the velocity of the block when x=\frac{A}{2}=0.0625 m

Now let's begin with the answers:

<h3>a) Mass of the block</h3>

We can solve this by the conservation of energy principle:

U_{o}+K_{o}=U_{f}+K_{f} (1)

Where:

U_{o}=k\frac{A^{2}}{2} is the initial potential energy

K_{o}=0  is the initial kinetic energy

U_{f}=k\frac{x^{2}}{2} is the final potential energy

K_{f}=\frac{1}{2} m V^{2} is the final kinetic energy

Then:

k\frac{A^{2}}{2}=k\frac{x^{2}}{2}+\frac{1}{2} m V^{2} (2)

Isolating m:

m=\frac{k(A^{2}-x^{2})}{V^{2}} (3)

m=\frac{7 N/m((0.125 m)^{2}-(0.0625 m)^{2})}{(0.32 m/s)^{2}} (4)

m=0.80 kg (5)

<h3>b) Period</h3>

The period T is given by:

T=2 \pi \sqrt{\frac{m}{k}} (6)

Substituting (5) in (6):

T=2 \pi \sqrt{\frac{0.80 kg}{7 N/m}} (7)

T=2.12 s (8)

<h3>c) Maximum acceleration</h3>

The maximum acceleration a_{max} is when the force is maximum F_{max}, as well :

F_{max}=m.a_{max}=k.x_{max} (9)

Being x_{max}=A

Hence:

m.a_{max}=kA (10)

Finding a_{max}:

a_{max}=\frac{kA}{m} (11)

a_{max}=\frac{(7 N/m)(0.125 m)}{0.80 kg} (12)

Finally:

a_{max}=1.093 m/s^{2}

You might be interested in
Explain Ionic and Covalent bonding..
Elis [28]
Ionic bonding is a type of chemical bonding that involves the electrostatic attraction between oppositely charged ions, and is the primary interaction occurring in ionic compounds.A covalent bond, also called a molecular bond, is a chemical bond that involves the sharing of electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding.
7 0
3 years ago
I need a little help with this
Mandarinka [93]

Answer:

truck 1 has the most velocity

Explanation:

Because it weights less which means it faster and yea

3 0
2 years ago
A mass spectrometer is being used to separate common oxygen-16 from the much rarer oxygen-18, taken from a sample of old glacial
Nataly_w [17]

Answer:

0.092 m

Explanation:

A charged moving particle immersed in a region with magnetic field follows a circular trajectory at constant speed (uniform circular motion), since the magnetic forces acts perpendicular to the direction of motion of the particle.

Since the magnetic force acts as centripetal force, we can write:

qvB=m\frac{v^2}{r}

where

q is the charge of the particle

v is its velocity

B is the strength of the magnetic field

m is the mass of the particle

r is the radius of the orbit

Solving the equation for r,

r=\frac{mv}{qB}

For the ion of oxygen-16, we have:

m_A=2.66\cdot 10^{-26}kg

q_A = 1.6\cdot 10^{-19}C (it is singly charged)

v_A=2.90\cdot 10^6 m/s

B_A=1.30 T

So the radius of its orbit is

r_A=\frac{m_A v_A}{q_A B_A}=\frac{(2.66\cdot 10^{-26})(2.90\cdot 10^6)}{(1.6\cdot 10^{-19})(1.30)}=0.371 m

For the ion of oxygen-18, we have:

m_B = \frac{18}{16}m_A = 2.99\cdot 10^{-26}kg

q_B = 1.6\cdot 10^{-19}C (it is singly charged)

v_B=2.90\cdot 10^6 m/s

B_B=1.30 T

So the radius of its orbit is

r_B=\frac{m_B v_B}{q_B B_B}=\frac{(2.99\cdot 10^{-26})(2.90\cdot 10^6)}{(1.6\cdot 10^{-19})(1.30)}=0.417 m

After each ion has travelled a semicircle, the separation between the two ions will be twice the difference in their radius, so:

d=2(r_B-r_A)=2(0.417-0.371)=0.092 m

3 0
2 years ago
A wooden block is sitting on an inclined plane near the bottom. The student gave the block a flick and it moved up the inclined
sladkih [1.3K]

Answer:

The block didn't slide due to balancing of gravitational force with friction force

Explanation:

When the block was given a flick the force provided an acceleration to it and it moved up the inclined plane. when the block reached top it was expected that it would slide back but it didn't this happened because of the frictional force acting on the bottom the block which was balancing the gravitational force component along the plane and this prevented sliding back of the block.

static friction  was balancing mg*sin(theta)

fs = mg*sin(theta)

6 0
2 years ago
640 nanometer setara dengan​
lidiya [134]

Answer:

640 nanometer setara dengan​ 6.4e-7 meter

7 0
2 years ago
Other questions:
  • The image of a distant tree is virtual and very small when viewed in a curved mirror. The image appears to be 22.9 cm behind the
    11·2 answers
  • A paratrooper is initially falling downward at a speed of 27.6 m/s before her parachute opens. When it opens, she experiences an
    6·1 answer
  • The four diagrams above show two magnets, X and Z. They are different distances apart in each diagram. In which diagram will mag
    9·2 answers
  • If the mass of a material is 45 grams and the volume of the material is 10 cm^3, what would the density of the material be
    9·1 answer
  • Wires 1, 2, and 3 each have current moving through them to the right. I1 = 10 A, I2 = 5 A, and I3 = 8 A. Wire 2 is 15 cm long an
    13·1 answer
  • How does the water cycle transport energy and matter
    15·1 answer
  • The temperature of 2.0 g of helium is increased at constant volume by ΔT. What mass of oxygen can have its temperature increased
    15·1 answer
  • Help plsssssssssss I write it 100 time no one answer
    15·1 answer
  • Which geologic events occur most often at this mid-oceanic ridge plate
    8·1 answer
  • Sound is capable of travelling in which medium or media ?<br><img src="https://tex.z-dn.net/?f=%20%5C%5C%20" id="TexFormula1" ti
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!