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irga5000 [103]
3 years ago
5

An object on a vertical spring oscillates up and down in simple harmonic motion with an angular frequency of 14.2 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:
zubka84 [21]3 years ago
7 0

Answer:

0.04865 m

Explanation:

k = Spring Constant

m = Mass

d = Distance

g = Acceleration due to gravity = 9.81 m/s²

Angular frequency is given by

\omega=\sqrt{\dfrac{k}{m}}\\\Rightarrow \dfrac{k}{m}=\omega^2\\\Rightarrow \dfrac{k}{m}=14.2^2

At equilibrium we have

kd=mg\\\Rightarrow d=\dfrac{mg}{k}\\\Rightarrow d=\dfrac{g}{\omega^2}\\\Rightarrow d=\dfrac{9.81}{14.2^2}\\\Rightarrow d=0.04865\ m

The distance by which the spring stretches from its unstrained length is 0.04865 m

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A bowling ball weighing 71.2 N is attached to the ceiling by a 3.70 m rope. The ball is pulled to one side and released; it then
amm1812

Answer:

a, 7.26kg

b, 36.59N

Explanation:

The question says it swings like a pendulum, as such, we would use the formula for circular acceleration.

a = v²/r

a = 4.2²/3.7

a = 17.64/3.7

a = 4.77m/s²

The acceleration of the ball is directed towards the centre because circular acceleration is usually directed towards the centre

To find tension, recall, F = ma

m = F/a

m = 71.2/9.81

m = 7.26kg

In solving for tension then, we use our acceleration to be (9.81 - 4.77) = 5.04m/s²

Tension = ma

Tension = 7.26 * 5.04

Tension = 36.5904

Hence the tension in the rope is 36.59N

5 0
3 years ago
When a certain amount of heat is supplied to 1KG of insulated aluminium. The temperature of the aluminium rises by 1°C
Bumek [7]

Answer:

The specific heat of aluminium is 897J/kg k . This values is almost 2.3 times of specific heat of copper .

Aluminium has higher thermal capacity than water

Explanation:

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6 0
3 years ago
Read 2 more answers
A bicycle pedal is pushed straight downwards by a foot with a 16 Newton force. The shaft of the pedal is 20 cm long. If the shaf
BartSMP [9]

Answer:

2.56 N*m

Explanation:

Torque is force times distance, with the force being perpendicular to the distance.

If the force and distance are not perpendicular, a projection of one of the two must be used instead.

We will use the projection of the length of the shaft upon a perpendicular of the force applied. This will have a magnitude of:

Lh = L * cos(a) (I name it Lh because it is a horizontal projection in this case)

Lh = 0.2 * cos(π/5) = 0.16 m

Then:

T = f * d

T = 16 * 0.16 = 2.56 N*m

6 0
3 years ago
What is motion? give 3 examples
Tomtit [17]

Answer:

Motion definition: the action or process of moving or being moved.

Examples:

1. moving a hand

2. riding a bicycle

3. running

8 0
3 years ago
A stone is launched vertically upward from a cliff 384 ft above the ground at a speed of 80 ft divided by s. Its height above th
goldenfox [79]

Answer:

2.5 seconds

Explanation:

s(t) = -16t^2 + 80t + 384

for

0≤t≤8

First we differentiate s(t) to get s'(t)

s'(t) = -32t + 80

Let us then find the critical point; thus we will equate s'(t) to zero and then search for values where s'(t) is undefined

s'(t) = -32t + 80 = 0

t = 80/32

t = 2.5 sec

Let us evaluate s at the critical points and end points

s(0) = -16(0)^2 + 80(0) + 384 = 384

s(2.5) = -16(2.5)^2 + 80(2.5) + 384 = 684

s(8) = -16(8)^2 + 80(8) + 384 = 0

Thus, the stone attains it maximum height of 684ft at at t=2.5s

3 0
4 years ago
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