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Dominik [7]
3 years ago
11

A fireworks shell is accelerated from rest to a velocity of 82.0 m/s over a distance of 0.400 m. (a) How long did the accelerati

on last
Physics
1 answer:
KatRina [158]3 years ago
6 0

Find the acceleration:

v² - u² = 2ax

(v = final velocity, u = initial velocity, a = acceleration, x = displacement)

(82.0 m/s)² - 0² = 2 a (0.400 m)

a = (82.0 m/s)² / (2 (0.400 m))

a = 8405 m/s²

Find the time:

x = ut + 1/2 at²

(t = time)

0.400 m = 0 + 1/2 (8405 m/s²) t²

t² = (0.400 m) / (1/2 (8405 m/s²))

t = √((0.400 m) / (1/2 (8405 m/s²)))

t ≈ 0.00976 s

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A spring on Earth has a 0.500 kg mass suspended from one end and the mass is displaced by 0.3 m. What will the displacement of t
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To solve this problem we will apply the concepts related to the Force of gravity given by Newton's second law (which defines the weight of an object) and at the same time we will apply the Hooke relation that talks about the strength of a body in a system with spring.

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F_k = F_{W,E}

kx_1 = mg

The extension of the spring due to the weight of the object on Moon is a value of x_2, then

kx_2 = mg_m

Recall that gravity on the moon is a sixth of Earth's gravity.

kx_2 = m\frac{g}{6}

kx_2 = \frac{1}{6} mg

kx_2 = \frac{1}{6} kx_1

x_2 = \frac{1}{6} x_1

We have that the displacement at the earth was x_1 = 0.3m, then

x_2 = \frac{1}{6} 0.3

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3 years ago
Consider two massless springs connected in parallel. Springs 1 and 2 have spring constants k1 and k2 and are connected via a thi
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Answer:

k1 + k2

Explanation:

Spring 1 has spring constant k1

Spring 2 has spring constant k2

After being applied by the same force, it is clearly mentioned that spring are extended by the same amount i.e. extension of spring 1 is equal to extension of spring 2.

x1 = x2

Since the force exerted to each spring might be different, let's assume F1 for spring 1 and F2 for spring 2. Hence the equations of spring constant for both springs are

k1 = F1/x -> F1 =k1*x

k2 = F2/x -> F2 =k2*x

While F = F1 + F2

Substitute equation of F1 and F2 into the equation of sum of forces

F = F1 + F2

F = k1*x + k2*x

= x(k1 + k2)

Note that this is applicable because both spring have the same extension of x (I repeat, EXTENTION, not length of the spring)

Considering the general equation of spring forces (Hooke's Law) F = kx,

The effective spring constant for the system is k1 + k2

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