Ask question

Ask question

All categories

2 years ago

15

3. A 64 lb weight stretches a spring 4 ft in equilibrium. The weight is initially displaced 6 inches above equilibrium and given

a downward velocity of 6 ft/sec. Find its displacement for t > 0 if the medium resists the motion with a force equal to 3 times the speed in ft/sec (that is, the damping constant c = 3). Note that there is no external force in this case.

1 answer:

Damm [24]2 years ago

6 0

Answer:

Explanation:

the solution is given in the attached pictures

You might be interested in

A toy rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 s. The rocket engine provides constant upward a

Dvinal [7]

Answer:

2.13 s

Explanation:

Hi!

At t = 0s the rocket is at rest in its platform, so the intial speed is zero. I f the acceleration is A, then the height Y, and the speed V are:

$Y=\frac{A}{2}t^2$

$V=At$

We nedd to find time T during which the rocket engine provides upward acceleration. We know that:

$64\;m=\frac{A}{2}T^2\\ 60\frac{m}{s} =AT\\$

With these 2 equations we can find A and T (dropping units for simplicity):

$A=\frac{60}{T} \\64 =\frac{30}{T} T^2=30T\\T=\frac{64}{30}\approx 2.13\;s$

4 0

2 years ago

A quantum system has three energy levels, so three wavelengths appear in its emission spectrum. the shortest observed wavelength

daser333 [38]

The wavelength emitted is indirectly proportional to the difference in the change in the energy level. For the wavelength 278 nm the change in energy level is significantly high. Further change in energy level is indicated by 454nm light but the difference in energy level for this wavelength to be emitted is not greater than the previous one. There is a possibility that these subsystems have now very low energy which should result in wavelengths ranging from 700 to 900 nm. There is another possibility that there is some metastable subsystems in the system which may cause LASER emission.

3 0

2 years ago

A small metallic bob is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizonta

shusha [124]

Answer:

19.99 kg m²/s

Explanation:

Angular Momentum (L) is defined as the product of the moment of Inertia (I) and angular velocity (w)

L = m r × v.

r and v are perpendicular to each other,

where r = lsinθ.

l = 2.4 m

θ= 34°

g = 9.8 m/s² and m = 5 kg

resolving using newtons second law in the vertical and horizontal components.

T cos θ − m g = 0

T sin θ − mw² lsin θ = 0

where T is the force with which the wire acts on the bob

w = √g / lcosθ

= √ 9.8 / 2.4 ×cos 34

= 2.2193 rad/s

the angular momentum L = mr× v

= mw (lsin θ)²

= 5 × 2.2193 (2.4 ×sin 34°)²

=19.99 kg m²/s

8 0

2 years ago

A woman makes 50% more than her husband. Together they make $2500 each month? How much does the woman earn each month?a) $950b)

Sergeeva-Olga [200]

Answer:b

Explanation:

Given

Woman earn 50% more than her husband

Total sum of their money is $=\$ 2500$

Suppose man earns $\$ P$

so women earns $P+0.5 P=P(1+0.5)=1.5 P$

Sum of their money is

$P+1.5 P=2500$

$P=\$ 1000$

Women earns $=1.5\times 1000=\$ 1500$

6 0

2 years ago

Two identical ladders are 3.0 m long and weigh 600 N each. They are connected by a hinge at the top and are held together by a h

ruslelena [56]

Answer:

The tension in the rope is 281.60 N.

Explanation:

Given that,

Length = 3.0 m

Weight = 600 N

Distance = 1.0 m

Angle = 60°

Consider half of the ladder,

let tension be T, normal reaction force at ground be F, vertical reaction at top hinge be Y and horizontal reaction force be X.

$Y+F=600$ ....(I)

$X=T$ .....(II)

On taking moment about base

$X\times l\cos\theta+Y\times l\sin\theta-F\dfrac{l}{2}\sin\theta-T\times d=0$

Put the value into the formula

$X\times3\cos30+Y\times3\sin30-600\times1.5\sin30-T\times1=0$

$3\cos30 T-T=600\times1.5\sin30-Y \times3\sin30$

$1.598T=450-1.5(600-F)$ ....(III)

We need to calculate the force for ladder

$2F=600\trimes 2$

$F=600\ N$

We need to calculate the tension in the rope

From equation (3)

$1.598T=450-1.5(600-600)$

$1.598T=450$

$T=\dfrac{450}{1.598}$

$T=281.60\ N$

Hence, The tension in the rope is 281.60 N.

7 0

2 years ago

Read 2 more answers