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Gnesinka [82]
3 years ago
9

A mass is hung from a spring and set in motion so that it oscillates continually up and down. The velocity v of the weight at ti

me t is given by the equation v=−2 cos(3πt) with v measured in feet per second and t measured in seconds. Determine the maximum velocity of the mass and the amount of time it takes for the mass to move from its lowest position to its highest position.
Physics
1 answer:
djverab [1.8K]3 years ago
8 0

Answer:

the maximum velocity of the mass v (max) = 2 ft/s

the amount of time it takes for the mass to move from its lowest position to its highest position∆t = 1/3 seconds = 0.33 seconds

Explanation:

Given the velocity equation;

v=−2 cos(3πt)

The maximum velocity would be at cos(3πt) = 1 or cos(3πt) = -1

v (max) = -2 × -1 = 2 ft/s

The time taken for the mass to move from lowest position to highest position

At Lowest position, vertical velocity equals zero.

At highest position, vertical velocity equals zero.

The time taken for the mass to move from one v = 0 to the next v = 0

Cos(π/2) = 0 and

Cos(3π/2) = 0

For the first;

Cos(3πt) = cos(π/2)

3πt1 = π/2

t1 = π/2(3π)

t1 = 1/6 second

For the second;

Cos(3πt) = cos(3π/2)

3πt2 = 3π/2

t2 = 3π/2(3π)

t2 = 1/2 second

∆t = t2 - t1 = 1/2 - 1/6 = 3/6 - 1/6 = 2/6 = 1/3 seconds

∆t = 1/3 seconds

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gizmo_the_mogwai [7]

Answer:

Acceleration,  767.08\ m/s^2

Explanation:

Given that,

Height from a ball falls the ground, h = 17.3 m

It is in contact with the ground for 24.0 ms before stopping.

We need to find the average acceleration the ball during the time it is in contact with the ground.

Firstly, find the velocity when it reached the ground. So,

v^2=u^2+2ah

u = initial velocity=0 m/s

a = acceleration=g

v=\sqrt{2gh} \\\\v=\sqrt{2\times 9.8\times 17.3} \\\\v=18.41\ m/s

It is in negative direction, u = -18.41 m/s

Let a is average acceleration of the ball. Consider, v = and u = -18.41 m/s.

a=\dfrac{v-u}{t}\\\\a=\dfrac{0-18.41}{24\times 10^{-3}}\\\\a=767.08\ m/s^2

So, the average acceleration of the ball during the time it is in contact is 767.08\ m/s^2.

4 0
3 years ago
If an exit sign is hanging from the ceiling by three chains each of which has a tension of 15N what is the weight of the sign
kvasek [131]
The weight is 45 N, because the three chains hold the sign, and each contributes 15 N.

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3 0
3 years ago
Jack drops a stone from rest off of the top of a bridge that is 24.4 m above the ground. After the stone falls 6.6 m, Jill throw
alukav5142 [94]
-17.555m/s

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then i found the velocity at 6.6m using vf^2 = vi^2 + 2ad
and I found the time it took to get to 6.6m, so that I knew how long Jill waited to throw her stone, I used the formula d = t(vi+vf)/2, then i done total time - the time she waited, to get the time it took for there stones to hit the ground at the same time.

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4 0
2 years ago
An object moves from the position +16m to the position +43m in 12s. What us the total displacement
NeX [460]

First method

initial distance = 16m

final distance= 43 m

total distance covered= final -initial

                                     =43m -16m

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Second method

Si= 16m

Sf =43 m

t= 12 s

first we will find V

V =  (Sf-Si)/ t

V =( 43- 16)/ 12

V = 27/12  ⇒ V= 9/4

V= distance / time

distance= V×time

distance = (9/4) ×12

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3 0
3 years ago
If a net force applied to an object is equal to zero, then the forces that are acting on an object are considered.
hjlf

Answer:

The mass will accelerate. Balanced Forces: When forces are in balance, acceleration is zero. Velocity is constant and there is no net or unbalanced force. A plane will fly at constant velocity if the acceleration is zero.

Explanation:

5 0
3 years ago
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