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3 years ago

11

One type of BB gun uses a spring-driven plunger to blow the BB from its barrel.

1 answer:

otez555 [7]3 years ago

8 0

Answer:

a, k=888.88N/m^2

b, f=133.33N

Explanation:

One type of BB gun uses a spring-driven plunger to blow the BB from its barrel.

(a) Calculate the force constant of its plunger’s spring if you must compress it 0.150 m to drive the 0.0500-kg plunger to a top speed of 20.0 m/s.

(b) What force must be exerted to compress the spring?

let's start by stating the parameters that are involved in this question

x=compression, 0.15m

velocity=20m/s

mass=0.05kg

to get the energy by the plunger

e=1/2mv^2

e=0.5*0.05*20^2

e=10J

the potential energy stored in the spring can be used to get the force constant

potential energy=1/2kx^2

10=0.5*k*0.15^2

0.0225k=20

k=888.88N/m^2

recall from hooke's law which states that the force applied on an elastic material is directly proportional to the extension/compression, as far as the elastic limit is not exceeded

f=kx

f=888.88*.15

f=133.33N, force exerted to compress the spring

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A spring with spring constant 11.5 N/m hangs from the ceiling. A 490 g ball is attached to the spring and allowed to come to res

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Answer:

The time constant is $\tau = 17.5 \ s$

Explanation:

From the question we are told that

The spring constant is $k = 11.5 \ N/m$

The mass of the ball is $m_b = 490 \ g = 0.49 \ kg$

The amplitude of the oscillation t the beginning is $x = 6.70 cm = 0.067 \ m$

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=> $t = 30 * 2 * 3.142 * \sqrt{\frac{ 0.490}{11.5} }$

=> $t = 38.88 \ s$

Generally the amplitude at time t is mathematically represented as

$x(t) = x e^{-\frac{at}{2m} }$

Here a is the damping constant so

at $t = 38.88 \ s$ , $x_t = 2.20 cm = 0.022 \ m$

So

$0.022 = 0.067 e^{-\frac{a * 38.88}{2 * 0.490} }$

=> $0.3284 = e^{-\frac{a * 38.88}{2 * 0.490} }$

taking natural log of both sides

=> $ln(0.3284 ) = -\frac{a * 38.88}{2 * 0.490} }$

=> $a = 0.028$

Generally the time constant is mathematically represented as

$\tau = \frac{m}{a}$

=> $\tau = \frac{0.490}{ 0.028}$

=> $\tau = 17.5 \ s$

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