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Elan Coil [88]
3 years ago
14

(a) A novelty clock has a 0.0100-kg-mass object bouncing on a spring that has a force constant of 1.25 N/ m. What is the maximum

velocity of the object if the object bounces 3.00 cm above and below its equilibrium position
Physics
1 answer:
ki77a [65]3 years ago
6 0

Answer:

0.3354 m/s

Explanation:

Using the general equation of a wave,

x(t) = Acos(ωt+Φ)....................... Equation 1

Where x(t) = distance of the wave at an instantaneous time t, A = maximum displacement of the wave, ω = angular velocity, t = time, Φ = phase angle.

Note: v(t) = x(t)/t, and this is the differentiation of x(t)

V(t) = -Aω sin(ωt+Φ)............. Equation 2

From the equation above,

V(max) = Aω............... Equation 3

But,

ω = √(k/m)................ Equation 4

Where k = force constant of the spring, m = mass of the object.

Given: k = 1.25 N/m, m = 0.01 kg

Substitute these values into equation 4.

ω = √(1.25/0.01)

ω = √125

ω = 11.18 rad/s

Also given: A = 3.00 cm = 0.03 m

Substitute into equation 3

V(max) = 11.18(0.03)

V(max) = 0.3354 m/s

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A world-class sprinter running a 100 m dash was clocked at 5.4 m/s 1.0 s after starting running and at 9.8 m/s 1.5 s later. In w
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Answer:

<em>The output power is greater in the interval from 1.0 s to 2.5 s</em>

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<u>Physical Power </u>

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\displaystyle P=\frac{W}{t}

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W=F.x

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F=m.a

being m the mass of the object and a the acceleration it has for a given period of time. In our problem, we have two different behaviors for each interval and we must calculate this force since the acceleration is changing. Let's calculate the acceleration in the first interval. We can use the formula for the final speed vf knowing the initial speed vo (which is 0 because the sprinter starts from rest), the acceleration a, and the time t:

v_f=v_o+at

v_f=at

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\displaystyle a=\frac{v_f}{t}={5.4}{1}

a=5.4\ m/s^2

The distance traveled in the interval is given by

\displaystyle x=v_o.t+\frac{a.t^2}{2}

Since vo=0

\displaystyle x=\frac{a.t^2}{2}=\frac{5.4(1)^2}{2}

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F=m.a

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W=F.x=2.7m(5.4)

W=14.58m

The power is finally computed

\displaystyle P=\frac{W}{t}=\frac{14.58m}{1}

P=14.58m

During the second interval, from t=1 sec to 1.5 sec, the speed changes from 5.4 m/s to 9.8 m/s. This allows us to compute the second acceleration

\displaystyle a=\frac{v_f-v_o}{t}=\frac{9.8-5.4}{0.5}

a=8.8\ m/s^2

The distance is

\displaystyle x=(5.4).(0.5)+\frac{8.8(0.5)^2}{2}

x=3.8\ m

The net force is

F=m(8.8)=8.8m

The work done by the sprinter is now computed as

W=8.8m(3.8)=33.44m

At last, the output power is

\displaystyle P=\frac{33.44m}{0.5}=66.88m

By comparing both results, and being m the same for both parts, we conclude the output power is greater in the interval from 1.0 s to 2.5 s

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