4.

A. The potential energy stored in the compressed spring of a dart gun, with a spring constant of 62.00 N/m, is 0.940 J. Find by

valina [46]

a. The spring is compressed by 0.174 m.

b. The vertical distance the dart travels from its position when the spring is compressed to its highest position is 9.6 m.

c. The horizontal velocity of the dart at that time is 13.74 m/s.

d. The horizontal distance from the equilibrium position at which the dart hits the ground is 19.236 m.

<h3>What is potential energy?</h3>

The energy by virtue of its position is called the potential energy.

a. Given is the potential energy stored in the compressed spring of a dart gun, with a spring constant of 62.00 N/m, is 0.940 J.

PE of spring = 1/2 kx²

Put the values, we get

P.E = 0.940 = 1/2 x 62 x²

x = 0.174 m

Thus, the spring is compressed by 0.174 m.

b. Given is a 0.010 kg dart is fired straight up.

The vertical height is find out by

0.940 J = (0.010 kg) (9.8 m/s²) h

h = 9.6 m

Thus, the vertical distance the dart travels from its position is 9.6 m

c. From the conservation of energy principle, total mechanical energy is conserved.

1/2 mv² =mgh

v = √2gh

Plug the values, we get

v = √2 x 9.8x 9.6

v = 13.74 m/s

Thus, the horizontal velocity is 13.74 m/s.

d. Time that dart spends in air, t = √2h/g

t = √(2x9.6)/9.81

t = 1.4 s

The horizontal distance from the equilibrium position at which the dart hits the ground.

Horizontal distance = (Velocity on x direction) x time

Horizontal distance = 13.74 m/s x 1.4s

Horizontal distance = 19.236 m

Thus, the horizontal distance is 19.236 m.

Learn more about potential energy.

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7 0

2 years ago

Discuss the relationship between electric and magnetic fields

erik [133]

Electric and magnetic field vectors are perpindicalar to each other in a electromagnetic wave. Passing stay current through a straight conductor shows some magnetic flux.

5 0

4 years ago

A 1000-kg whale swims horizontally to the right at a speed of 6.0 m/s. It suddenly collides directly with a stationary seal of m

anzhelika [568]

Answer:

Momentum after collision will be 6000 kgm/sec

Explanation:

We have given mass of the whale = 1000

Initial velocity v = 6 m/sec

It collides with other mass of 200 kg which is at stationary

Initial momentum of the whale = 1000×6 = 6000 kgm/sec

We have to find the momentum after collision

From conservation of momentum

Initial momentum = final momentum

So final momentum = 6000 kgm/sec

5 0

3 years ago

The position of a particle moving along the x axis depends on the time according to the equation x = ct² - bt³, where x is in me

Kamila [148]

Answer:

(a) $\frac{m}{s^2}$

(b) $\frac{m}{s^3}$

(c) 1 s

(d) 20 m

(e) 1 m

(f) $0\frac{m}{s}$

(g) $-12\frac{m}{s}$

(h) $-36\frac{m}{s}$

(i) $-72\frac{m}{s}$

(j) $-6\frac{m}{s^2}$

(k) $-18\frac{m}{s^2}$

(l) $-30\frac{m}{s^2}$

(m) $-42\frac{m}{s^2}$

Explanation:

Since x is measured in meters and t in seconds, constants a and b must have units that gives meters when multiplied by square and cubic seconds respectivly, so that would mean $\frac{m}{s^2}$ for a and $\frac{m}{s^3}$ for b.

We can get the velocity v equation by deriving the position with respect to t, which gives:

$v=6*t-6*t^2$

And the acceleration a equation by deriving again:

$a=6-12*t$

Now for getting the maximun position between 0 and 4, we must find to points where the positions first derivate is equal to cero and evaluate those points. That is v=0, which gives

$6*t-6*t^2=0\\6t*(1-t)=0\\t=0 or t=1$

For t = 0, x = 0 so the maximun position is archieved at 1 second, which gives x = 1 meter.

For obtaining it's displacement r, we can integrate the velocity from 0 seconds to 4 seconds, which gives the mean value of the position in that interval:

$r=\frac{1}{4}*(2*4^3-3*4^2)m\\r= 20m$

For the remaining questions, we just replace the values of t on the respective equations.

8 0

4 years ago

You just tested the hypothesis a proposed model for the position of bright fringes produced by two slits. Explain what the model

Viefleur [7K]

Answer:

two-slit interference model was proposed by Young d sin θ = m λ

Explanation:

The two-slit interference model was proposed by Young, it establishes that if a coherent source of light passes through two slits, the shape of the given pattern is a consequence of the relative phase difference between the two rays; mathematically it can be expressed by

d sin θ = m λ

m= 0, 1, 2, 3, ...

for constructive interference, that is, the two rays arrive with a number between wavelengths.

D is the distance between the slits, tea the angle between the two rays, m an integer and m the wavelength used.

In a simulation a pattern of slits of equal intensity and equally spaced is observed.

3 0

3 years ago