Physics, 29.10.2020 17:00 tylorroundy

Problem 6 (20 points) A ballistic pendulum is a device often used for measuring the velocity of a projectile. Assume to projectile fully embeds itself in the pendulum. If the projectile mass is 25 grams, the pendulum mass is 2.5 kg, and the vertical displacement of the pendulum after the collision is 12 cm, find the velocity of the projectile just prior to the collision.

Answers: 2

Show answers

Answers

Answer from: galaalexa

The velocity of the projectile just prior to the collision is 154.934 meters per second.

Explanation:

Let consider the projectile-pendulum system as our system of study, from statement we know that projectile gives kinetic energy to the pendulum and turns into gravitational potential energy. By Principle of Energy Conservation we construct the following expression:

$U_{g,1}+K_{1} = U_{g,2}+K_{2}$ (Eq. 1)

Where:

$U_{g,1}$ , $U_{g,2}$ - Initial and final gravitational potential energies, measured in joules.

$K_{1}$ , $K_{2}$ - Initial and final kinetic energies, measured in joules.

By applying definitions of gravitational potential and kinetic energies, we expand and simplify the equation above:

$(m+M)\cdot g \cdot (y_{2}-y_{1}) = \frac{1}{2}\cdot (m+M)\cdot (v_{1}^{2}-v_{2}^{2})$

$g\cdot (y_{2}-y_{1})=\frac{1}{2}\cdot (v_{1}^{2}-v_{2}^{2})$

And we clear the initial velocity of the pendulum-projectile system:

$v_{1}=\sqrt{v_{2}^{2}+2\cdot g\cdot (y_{2}-y_{1})}$ (Eq. 2)

Where:

- Mass of the projectile, measured in kilograms.

- Mass of the ballistic pendulum, measured in kilograms.

$v_{1}$ , $v_{2}$ - Initial and final speeds of the pendulum-projectile system, measured in meters per second.

- Gravitational acceleration, measured in meters per square second.

$y_{1}$ , $y_{2}$ - Initial and vertical position of the pendulum-projectile system, measured in meters.

Under the consideration of inellastic collision, we find the velocity of the projectile prior to the collision by Principle of Linear Momentum Conservation:

$m\cdot v_{o, P} + M\cdot v_{o,B} = (m+M)\cdot v_{1}$

$v_{o,P} = \frac{(m+M)\cdot v_{1}-M\cdot v_{o,B}}{m}$ (Eq. 2)

Where:

$v_{o, P}$ - Velocity of the project prior to the collision, measured in meters per second.

$v_{o,B}$ - Velocity of the ballistic pendulum prior to the collision, measured in meters per second.

If we know that $v_{2} = 0\,\frac{m}{s}$ , $g = 9.807\,\frac{m}{s^{2}}$ , $y_{2}-y_{1} = 0.12\,m$ , $m = 0.025\,kg$ , $M = 2.5\,kg$ and $v_{o,B} = 0\,\frac{m}{s}$ , then the velocity just prior to the collision is:

By (Eq. 1):

$v_{1} =\sqrt{\left(0\,\frac{m}{s} \right)^{2}+2\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (0.12\,m)}$

$v_{1} \approx 1.534\,\frac{m}{s}$

By (Eq. 2):

$v_{o,P} = \frac{(0.025\,kg+2.5\,kg)\cdot \left(1.534\,\frac{m}{s} \right)-(2.5\,kg)\cdot \left(0\,\frac{m}{s} \right)}{0.025\,kg}$

$v_{o,P} = 154.934\,\frac{m}{s}$

The velocity of the projectile just prior to the collision is 154.934 meters per second.

Answer from: Quest

the electric field is a “force field” around a charged object that illustrates the direction the electric force would push an imaginary

Answer from: Quest

He can play two games. 13/4=3.253.25*2=6.5

Another question on Physics

Physics, 22.06.2019 01:40

Lin yao looks at the back of a spoon. how should she describe her reflection? upside down and smaller upside down and larger right-side up and smaller right-side up and larger

Answers: 1

Answer

Physics, 22.06.2019 03:00

If a spring has a k value of 100 newtons per meter and it is stretched 0.50 meters, what is the restoring force of the spring?

Answers: 2

Answer

Physics, 22.06.2019 10:40

When the magnetic domains in a material can be aligned, but eventually drift out of alignment, the material is

Answers: 2

Answer

Physics, 22.06.2019 14:40

A5 foot by 5 foot box culvert is buried 6 feet beneath the surface of the ground. a crosssection of this very long culvert (into and out of the page) is illustrated below. assume that the soil in which the culvert is buried has the following properties: jt = 120 pcf, w = 12%, ko = 0.50, ka = 0.33, and kp = 3.00. calculate the total horizontal force per unit length of culvert (fh) felt on one of the vertical faces of the culvert.

Answers: 1

Answer

You know the right answer?

Problem 6 (20 points) A ballistic pendulum is a device often used for measuring the velocity of a pr...

Questions