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sineoko [7]
3 years ago
15

The motion of a particle is described by x = 10 sin (πt + π/3), where x is in meters and t is in seconds. At what time in second

s is the potential energy equal to the kinetic energy?
Physics
1 answer:
OverLord2011 [107]3 years ago
7 0

Answer:

5/12

Explanation:

Given

x = 10 sin (πt + π/3)

v = distance/time

So, v = dx/dt

Differentiating x with respect to t

v = 10π cos(πt + π/3)

Also,

½kx² = ½mv²

Substituting values for x and v in the above equation

½k(10sin (πt + π/3))² = ½m(10πcos(πt + π/3))²

Divide through by ½

k(10sin (πt + π/3))² = m(10πcos(πt + π/3))²

Open both bracket

100ksin²(πt + π/3) = 100mπ²cos²(πt + π/3)

Divide through by 100

ksin²(πt + π/3) = mπ²cos²(πt + π/3)

Divide through by kcos²(πt + π/3)

ksin²(πt + π/3) ÷ kcos²(πt + π/3) = mπ²cos²(πt + π/3) ÷ kcos²(πt + π/3)

tan²(πt + π/3) = mπ²/k

tan²(πt + π/3) = (m/k)π²

But w² = k/m and w = 2π/T

(2π/T)² = k/m

(2π)²/T² = k/m

1/T² = k/m ÷ (2π)²

1/T² = k/m*(2π)²

T² = m(2π)²/k

From the Question, T is when πt = 2π or T = 2

Substitute 2 for T in the above equation

2² = m(2π)²/k

4 = m(2π)²/k

4 = 4π²m/k

m/k = 1/π²

(m/k)π² = 1

Remember that tan²(πt + π/3) = (m/k)π²

So, tan²(πt + π/3) = 1

This gives

πt + π/3 = 45° = π/4

πt + π/3 = π/4

Divide through by π

t + ⅓ = ¼

t = ¼ - ⅓

t = -1/12 --- Negative

Using the second quadrant

πt + π/3 = 3π/4

Divide through by π

t + ⅓ = ¾

t = ¾ - ⅓

t = 5/12

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3 years ago
A 12.65 g sample of a radioactive substance is allowed to decay for 17.22 min. At that time, the sample weighed 3.115 g. What is
Mademuasel [1]

Answer:

8.61 min

Explanation:

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total time for decay =17.22

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8 0
2 years ago
A soccer ball is kicked At 8m/s. It lands on the ground after being in the air for .85 seconds. At what angle is it kicked?
SpyIntel [72]

If ball remains in air for total time T = 0.85 s

this is also known as time of flight

In order to find the time of flight we can use kinematics

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v_y = 4.165 m/s

now we know that net velocity of the ball is 8 m/s

while is y direction component we got is vy = 4.165 m/s

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8 0
3 years ago
If you exert a force on an object in motion you will change its ____.
devlian [24]

If you exert a force on an object in motion, then depending on the
direction of the force you exert and the direction in which it's already
moving, you may speed it up, slow it down, or change the direction
of its motion. Any of these changes is called an acceleration. 

In addition to that, you'll change the object's momentum and kinetic energy.
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4 0
2 years ago
Read 2 more answers
A block rests on a frictionless table on Earth. After a 40-N horizontal force is applied to the block, it accelerates at 9.2 m/s
Paul [167]

Answer:

4.6 \frac{m}{s^2}

Explanation:

Since the table is frictionless, there is no force of dynamic  friction between table an block when the horizontal force is applied to it on Earth. Exactly the same is true when the table is taken to the Moon. Therefore, the Net Force acting on the object in both cases when the object accelerates, is the external horizontal force.

Notice that on Earth and on the Moon, the weight of the object (vertical and pointing up) is compensated by the normal force of the table on the object (pointing up and of the same magnitude as the weight) that precludes movement in the vertical direction. So in both cases, its acceleration will only be due to the horizontal force.

We use the equation for Net Force to find the mass of the object:

F=m*a\\40 N =m * 9.2 \frac{m}{s^2}\\\frac{40}{9.2} kg=m\\m=\frac{40}{9.2} kg

We use this mass (since the mass of the object is a constant independent of where the object is) to find the acceleration the object will experience when the 20 N horizontal force is applied on it on the Moon:

f=m*a\\20N=\frac{40}{9.2} kg*a\\20*9.2=40*a\\\frac{20*9.2}{40} =a\\a=\frac{9.2}{2} \frac{m}{s^2} \\ a=4.6 \frac{m}{s^2}

3 0
3 years ago
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