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kompoz [17]
3 years ago
10

A ball whose mass is 1.9 kg is suspended from a spring whose stiffness is 8.0 N/m. The ball oscillates up and down with an ampli

tude of 17 cm. Part 1 (a) What is the angular frequency? ω= radians/s the tolerance is +/-2% By accessing this Question Assistance, you will learn while you earn points based on the Point Potential Policy set by your instructor.
Physics
1 answer:
MArishka [77]3 years ago
4 0

Answer:

2.05 radians/s

Explanation:

This is a simple harmonic motion. The angular frequency of a loaded spring is given by

\omega = \sqrt{\dfrac{k}{m}}

where k is the spring constant and m is the mass on the spring.

Using the known values,

\omega = \sqrt{\dfrac{8}{1.9}} = 2.05

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A particle moves along a line so that its velocity at time t is v(t) = t2 − t − 20 (measured in meters per second). (a) Find the
Genrish500 [490]

Answer:

Displacement is 47,166667 meters, Distance traveled is 78.5 meters.

Explanation:

Let's remberi that v(t) = \frac d{dt}s(t). Distance traveled will be \int\limits^{10}_1 v(t) \, dt, while displacement will be \int\limits^{10}_1 |v(t)| \, dt (note the absolute value is needed because part of the movement MIGHT be backwards, which will add to the distance traveled, ie the number of steps, but does not contribute to displacement - think of a guy running in cirles).

Distance: \int\limits^{10}_1 {t^2-t-20} dt =(\frac13 t^3 - \frac12 t^2 -20t )\limits^{10}_1 = (\frac 13 *1000 - \frac12*100-20*10) - (\frac13 -\frac 12 -20) = \frac{2000-300-1200-2+3+60}6 = \frac{561}6 =78.5

Displacement: absolute value makes things a bit more annoying: v(t) is negative between t=1 and t=5 - the particle is moving backwards. The integral becomes:

\int\limits^{10}_1 |v(t)| \, dt = -\int\limits^5_1t^2-t-20\,dt +\int\limits^{10}_5t^2-t-20\, dt =\\-(\frac13 t^3 -\frac12 t^2-20t)\limits^5_1 +(\frac13 t^3 -\frac12 t^2-20t)\limits^{10}_5 =\\ -(\frac13*125-\frac1/2*25-20*5)+(\frac13-\frac12-20)+(\frac13*1000-\frac12*100-20*10)-(\frac13*125-\frac1/2*25-20*5) = 289/6 = 48,166667

Puff, pant, that should be it, please double check calculations, just in case.

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