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Ulleksa [173]
3 years ago
11

. A 1.50kg mass on a spring has a displacement as a function of time given by the equation: x(t) = (7.40cm)cos[(4.16s-1)t – 2.42

]. Find, a) the time for one complete vibration; b) the force constant of the spring; c) the maximum speed of the mass; d) the maximum force on the mass; e) at t= 1.00s, find the mass is a. the position, b. the speed, c. the acceleration d. the force on the mass
Physics
1 answer:
rusak2 [61]3 years ago
5 0

Answer:

Solution:

we have given the equation of motion is x(t)=8sint [where t in seconds and x in centimeter]

Position, velocity and acceleration are all based on the equation of motion.

The equation represents the position.  The first derivative gives the velocity and the 2nd derivative gives the acceleration.

x(t)=8sint

x'(t)=8cost

x"(t)=-8sint

now at time t=2pi/3,

position, x(t)=8sin(2pi/3)=4*squart(3)cm.

velocity, x'(t)=8cos(2pi/3)==4cm/s

acceleration, x"(t)==8sin(2pi/3)=-4cm/s^2

so at present the direction is in y-axis.

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Which change increases the electric force between objects?
Brrunno [24]
Well, the force is proportional to the product of the charges
on the two objects.  So if the objects are already negatively
charged distance between them is unchanged, then adding
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3 0
3 years ago
Read 2 more answers
reviews the approach taken in problems such as this one. A bird watcher meanders through the woods, walking 0.916 km due east, 0
Verizon [17]

Answer:

Displacement: 2.230 km    Average velocity: 1.274\frac{km}{h}

Explanation:

Let's represent displacement by the letter S and the displacement in direction 49.7° as A. Displaement is a vector, so we need to decompose all the bird's displacement into their X-Y compoments. Let's go one by one:

  • 0.916 km due east is an horizontal direction and cane be seen as  direction towards the negative side of X-axis.
  • 0.928 km due south is a vertical direction and can be seen as a direction towards the negative side of Y-axis.
  • 3.52 km in a direction of 49.7° has components on X and Y  axes. It is necessary to break it down using trigonometry,

First of all. We need to sum all the X components and all the Y componets.

∑Sx = Ax -0.916 ⇒  ∑Sx = [tex]3.52cos(49.7) - 0.916

∑Sx = 1.361 km

∑Sy = Ay - 0.918 ⇒ ∑Sy = 3.52sin(49.7) - 0.918

∑Sy = 1.767

The total displacement is calculated using Pythagoeran therorem:

S_{total} =\sqrt{Sx^{2}+ Sy^{2} } ⇒

S_{total} = 2.230 km

With displacement calculated, we can find the average speed as follows:

V = S/t  ⇒  V = \frac{2.230}{1.750}

V = 1.274\frac{km}{h}

7 0
3 years ago
Give two examples of events that show that the speed of sound is very much slower than the speed of light
jeka94

Answer:

1) Lightning, you see the lightning first and then hear the thunder.

2)When a person far away from you hits a ball with a bat, you can see them striking the ball first and then you will hear the sound of ball striking against the bat.

6 0
3 years ago
A charge q1 of -5.00 x 10^-9 C and a charge q2 of -2.00x 10^-9 C are separated by a distance of 40.0 cm. Find the equilibrium po
aleksandrvk [35]

Answer:

Explanation:

Let the equilibrium position of third charge be x distance from q₁.

Force on third charge due to q₁

= 9 x 10⁹ x 5 x 10⁻⁹ x 15 x 10⁺⁹ / x²

Force on third charge due to q₂

= 9 x 10⁹ x 2 x 10⁻⁹ x 15 x 10⁺⁹ /( .40-x)²

Both the force will act in opposite direction and for balancing , they should be equal.

9 x 10⁹ x 5 x 10⁻⁹ x 15 x 10⁺⁹ / x² = 9 x 10⁹ x 2 x 10⁻⁹ x 15 x 10⁺⁹ /( .40-x)²

5  / x² = 2 / ( .4 - x )²

Taking square root on both sides

2.236 / x = 1.414 / .4 - x

2.236 ( .4 - x ) = 1.414 x

.8944 - 2.236 x = 1.414 x

.8944 = 3.65 x

x = .245 m

24.5 cm

So the third charge should be at a distance of 24.5 cm from q₁ .

4 0
3 years ago
A long, thin straight wire with linear charge density λ runs down the center of a thin, hollow metal cylinder of radius R. The c
Delvig [45]

Answer:

E=\dfrac{\lambda }{2\pi \varepsilon _or}

Explanation:

Given that

For straight wire

Charge density= λ

For hollow metal cylinder

Charge density=2 λ

We know that electric filed for wire given as

E_w=\dfrac{\lambda_{wire} }{2\pi \varepsilon _or}

E_w=\dfrac{\lambda }{2\pi \varepsilon _or}

Now the electric filed due to hollow metal cylinder

E_c=\dfrac{\lambda_{cylinder} }{2\pi \varepsilon _or}

E_c=\dfrac{2\lambda }{2\pi \varepsilon _or}

Now  by considering the Gaussian surface r<R then only electric fild due to wire will present.So

At r<R

E=\dfrac{\lambda }{2\pi \varepsilon _or}

5 0
4 years ago
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