2 years ago

A cyclist rides in a circle with speed 8.1 m/s. What is his centripetal

1 answer:

5 0

Explanation:

We know that the tangent velocity is 8.1 m/s. We also know that the tangent velocity can be written in the following way:

Vt = ωr with ω being the angular velocity.

We now calculate ω:

ω = Vt/r = 8.1 m/s / 27m = 0.3 rad/s

Now that we have ω we can calculate the centripetal aceleration:

a = ω^2 * r = ( 0.3 )^2 * 27 = 2.43 m/s^2

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The nutritional calorie (Calorie) is equivalent to 1 kilocalorie. One pound of body fat is equivalent to about 4.10 × 103 Calori

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3 years ago

Exactly one turn of a flexible rope with mass m is wrapped around a uniform cylinder with mass M and radius R.

Dennis_Churaev [7]

Answer:

$\omega=\sqrt{\omega_0^2(\frac{M+m}{M})}$

Explanation:

The rotational kinetic energy when the cylinder is with the rope is:

$E_k=\frac{1}{2}I_c\omega_0^2+\frac{1}{2}I_r\omega_0^2$

where we used the fact that both rope and cylinder hast the same w. This E_k must conserve, that is, E_k must equal E_k when the rope leaves the cylinder. Hence, the final w is given by:

$E_{k1}=E_{k2}\\\\\frac{1}{2}I_c\omega_0^2+\frac{1}{2}I_r\omega_0^{2}=\frac{1}{2}I_c\omega^2\\\\\omega=\sqrt{\omega_0^2(\frac{I_c+I_r}{I_c})}$ (1)

For Ic and Ir we can assume that the rope is a ring of the same radius of the cylinder. Then, we have:

$I_c=\frac{1}{2}MR^2\\\\I_r=mR^2$

Finally, by replacing in (1):

$\omega=\sqrt{\omega_0^2(\frac{M+m}{M})}$

hope this helps!!

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3 years ago

An object is dropped from a height of 25 meters. At what velocity will it hit the ground? A. 7.0 meters/second B. 11 meters/seco

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$Final^{2}=Initial^{2}+2ad \\ x^{2}=0^{2}+2(9.8)(25) \\ x^{2}=490 \\ x=22.13 \\ C$

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3 years ago

An elevator accelerates upward at 1.2 m/s 2 . the acceleration of gravity is 9.8 m/s 2 . what is the upward force exerted by the

Marysya12 [62]

We can find the force by using the following formula;
N = ma + mg
Fa = ma = 76 x 1.2 = 91.2
Fg = mg = 76 x 9.8 = 744.8
N = 91.2 + 744.8 = 836
So, the force is 836 N.

8 0

3 years ago