Physics, 19.08.2019 21:30 alexisbreton

Arifle bullet with mass 8.00 g strikes and embeds itself in a block with a mass of .992 kg that rests on a frictionless, horizontal surface and it attached to a coil spring. the impact compresses the spring 15.0 cm. calibration of the spring shows that a force of 0.750 n is required to compress the spring 0.250 cm. find the magnitude of the block's velocity just after impact and the initial speed of the bullet.

Answers: 1

Show answers

Answers

Answer from: lee9724

Ok, so this problem has to be solved in a couple of different steps. This involves conservation of energy and conservation of momentum.
Step 1, find the spring coefficient with the given information: F=kx.
0.75N=k*0.250cm (don't forget to convert units!) => 0.75 = k*0.0025m
k = 300 N/m.
Step 2, from the spring coefficient, you can see how much energy is stored in the spring from the impact. Spring Energy = 0.5*k*x^2 = 0.5*300*(0.15^2) = 3.375Nm
Step 3, using conservation of energy, the only thing the stored energy in the spring came from is the bullet before the impact. Nothing was moving before the bullet struck the block and the spring was relaxed. Kinetic Energy of the bullet = 0.5*m*v^2 = 0.5 * 0.008 * (v^2) = 3.375 (remember to use unit conversion to get everything into N, m, kg!) SO! v^2 = 843.75 and v = 29.05 m/s
Step 4, now that you have pre-impact velocity of the bullet, use conservation of momentum to find the post impact velocity of the bullet plus block. m_total*v_result = m_bullet*v_bullet + m_block*v_block In this case, the v_block =0 and v_bullet is the v we solved for in step 3.
Plugging in the numbers: m_total = 1, m_bullet = 0.008, v_bullet = 29.05
v_result = 0.008*29.05/1 = 0.2324 m/s

Answer from: tacoursey1987p6xy9s

The magnitude of the block's velocity just after impact is about 2.60 m/s.

The initial speed of the bullet is about 325 m/s

$\texttt{ }$

Further explanation

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

$\large {\boxed {F = ma }$

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

$\texttt{ }$

Given:

mass of bullet = m₁ = 8.00 gram = 8 × 10⁻³ kg

mass of block = m₂ = 0.992 kg

initial speed of block = u₂ = 0 m/s

compression of spring = x = 15.0 cm = 0.15 m

spring constant = k = 0.750 ÷ (2.5 ×10⁻³) = 300 N/m

Asked:

final speed of block = v₂ = ?

initial speed of bullet = u₁ = ?

Solution:

Let:

final speed of the block just after impact = final speed of the bullet just after impact = v

Firstly , we will use Conservation of Energy as follows:

Ek = Ep

$\frac{1}{2}(m_1 + m_2)v^2 = \frac{1}{2} k x^2$

(m_1 + m_2) v^2 = k x^2

$(0.008 + 0.992) v^2 = 300 \times 0.15^2$

v^2 = 6.75

$v = \frac{3}{2}\sqrt{3} \texttt{ m/s}$

$v \approx 2.60 \texttt{ m/s}$

The magnitude of the block's velocity just after impact is about 2.60 m/s

$\texttt{ }$

Next , we will use Conservation of Momentum Law as follows:

m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2

$0.008u_1 + 0.992(0) = 0.008(\frac{3}{2}\sqrt{3}) + 0.992(\frac{3}{2}\sqrt{3})$

$0.008u_1 = \frac{3}{2}\sqrt{3}$

$u_1 \approx 325 \texttt{ m/s}$

The initial speed of the bullet is about 325 m/s

$\texttt{ }$

Learn moreImpacts of Gravity : Effect of Earth’s Gravity on Objects : The Acceleration Due To Gravity : Newton's Law of Motion: Example of Newton's Law:

$\texttt{ }$

Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

$\texttt{ }$

Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant

Arifle bullet with mass 8.00 g strikes and embeds itself in a block with a mass of .992 kg that rest

Answer from: Quest

What are the choices?

Answer from: Quest

i dont think you are wrong for wanting to get even with someone who did you wrong.

(i'm an eye for an eye kind of person) but if this person hurt you in a sexual way, i dont suggest doing anything to him. he should be taken to the proper authorities, you could go to jail depending on what you do. if it was something small like your sibling took your spot on the couch, than yea, i would get even with him by taking one of his favorite snacks lol. but i dont suggest you doing anything illegal.

Another question on Physics

Physics, 22.06.2019 05:10

Which diagram correctly demonstrates the various forces acting on a ball moving horizontally with some speed?

Answers: 2

Answer

Physics, 22.06.2019 12:30

As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. when you push the platform, you compress the springs. you do an amount of work of 79.0 j when you compress the springs a distance of 0.230 m from their uncompressed length. (a) what magnitude of force must you apply to hold the platform in this position? (b)how much additional work must you do to move the platform a distance 0.230 m farther? (c) what maximum force must you apply to move the platform a distance 0.230 m farther?

Answers: 1

Answer

Physics, 22.06.2019 15:00

When is a current produced? when the terminals of an electrochemical cell are connected by a wire if the electric circuit is opened in an electrochemical cell if the electrolyte is removed from an electrochemical cell when the electrodes are reversed in an electrochemical cell

Answers: 1

Answer

Physics, 22.06.2019 16:40

An owl dives toward the ground with a constant velocity of 4.40 m/s at 53.0° below the horizontal. the sun is directly overhead and casts a shadow of the owl directly below it. what is the speed (in m/s) of its shadow on level ground?

Answers: 3

Answer

You know the right answer?

Arifle bullet with mass 8.00 g strikes and embeds itself in a block with a mass of .992 kg that rest...

Questions