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fenix001 [56]
3 years ago
8

An object on a vertical spring oscillates up and down in simple harmonic motion with an angular frequency of 25.7 rad/s. Calcula

te the distance d by which the spring stretches from its unstrained length when the object is allowed to hang stationary from it.
Physics
1 answer:
Sergio [31]3 years ago
6 0

Answer:

The distance by which the spring stretches is 1.48 cm.

Explanation:

Given that,

An object on a vertical spring oscillates up and down in simple harmonic motion with an angular frequency of 25.7 rad/s, \omega=25.7\ rad/s

We know that angular frequency in SHM is given by :

\omega=\sqrt{\dfrac{k}{m}} \\\\\omega^2=\dfrac{k}{m}\\\\\dfrac{k}{m}=(25.7)^2.............(1)

When the object is allowed to hang stationary from it, the force due to spring is balanced by its weight. Such that :

kd=mg\\\\d=\dfrac{g}{(k/m)}

From equation (1) :

d=\dfrac{9.8}{(25.7)^2}\\\\d=0.0148\ m\\\\d=1.48\ cm

So, the distance by which the spring stretches is 1.48 cm.

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3 0
2 years ago
A block lies on a horizontal frictionless surface. A horizontal force of 100 N is applied to the block giving rise to an acceler
KIM [24]

Answer:

(a) m = 33.3 kg

(b) d = 150 m

(c) vf = 30 m/s

Explanation:

Newton's second law to the block:

∑F = m*a Formula (1)

∑F : algebraic sum of the forces in Newton (N)

m : mass s (kg)

a : acceleration  (m/s²)

Data

F= 100 N

a= 3.0 m/s²

(a) Calculating of the  mass of the block:

We replace dta in the formula (1)

F = m*a

100 =  m*3

m = 100 / 3

m = 33.3 kg

Kinematic analysis

Because the block  moves with uniformly accelerated movement we apply the following formulas:

d= v₀t+ (1/2)*a*t² Formula (2)

vf= v₀+a*t   Formula (3)

Where:  

d:displacement in meters (m)  

t : time interval in seconds (s)

v₀: initial speed in m/s  

vf: final speed in m/s  

a: acceleration in m/s²

Data

a= 3.0 m/s²

v₀= 0

t = 10 s

(b) Distance the block will travel if the force is applied for 10 s

We replace dta in the formula (2):

d= v₀t+ (1/2)*a*t²

d = 0+ (1/2)*(3)*(10)²

d =150 m

(c) Calculate the speed of the block after the force has been applied for 10 s

We replace dta in the formula (3):

vf= v₀+a*t

vf= 0+(3*(10)

vf= 30 m/s

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3 years ago
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Answer:

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Explanation:

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