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3 years ago

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2) Two ice skaters have masses m1 and m2 and are initially stationary. Their skates are identical. They push against one another

and move in opposite directions with different speeds. While they are pushing against each other, any kinetic frictional forces acting on their skates can be ignored. However, once the skaters separate, kinetic frictional forces eventually bring them to a halt. As they glide to a halt, the magnitudes of their accelerations are equal, and skater 1 glides twice as far as skater 2. What is the ratio m1/m2 of their masses

1 answer:

worty [1.4K]3 years ago

6 0

Answer:

m_1 / m_2 = sqrt (1 / 2)

Explanation:

Given:

- Initial velocity of both skaters V_i = 0

- Velocity of skater 1 after push = V_1

- Velocity of skater after push = V_2

- Distance traveled by skater 1 = s_1

- Distance traveled by skater 2 = s_2

- s_1 = 2*s_2

- Accelerations of both skaters to halt is equal

Find:

What is the ratio m1/m2 of their masses

Solution:

- Apply conservation of momentum for two skaters just before and after the push as follows:

P_i = P_f

0 = m_1*V_1 - m_2*V_2

- Evaluate: m_1 / m_2 = ( V_2 / V_1 )

- Apply Conservation of Energy on both skaters as follows:

- Skater 1:

0.5*m_1*V_1^2 = u_k*m_1*g*s_1

-Simplify: 0.5*V_1^2 = u_k*g*(2*s_2)

- Skater 2:

0.5*m_2*V_2^2 = u_k*m_2*g*s_2

-Simplify: 0.5*V_2^2 = u_k*g*s_2

- Divide the two energy equations for skaters:

(V_1 / V_2)^2 = 2

(V_2 / V_1)^2 = 1 / 2

- simplify: (V_2 / V_1) = sqrt (1 / 2)

-Hence from earlier momentum conservation results:

m_1 / m_2 = ( V_2 / V_1 ) = sqrt (1 / 2)

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To throw the discus, the thrower holds it with a fully outstretched arm. Starting from rest, he begins to turn with a constant a

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<u>Complete Question:</u>

To throw the discus, the thrower holds it with a fully outstretched arm. Starting from rest, he begins to turn with a constant angular acceleration, releasing the discus after making one complete revolution. The diameter of the circle in which the discus moves is about 1.9 m.

If the thrower takes 1.0 s to complete one revolution, starting from rest, what will be the speed of the discus at release?

<u>Answer:</u>

11.94 m/s will be the speed of the discus at release.

<u>Explanation:</u>

Given data:

Time taken to complete one revolution = 1.0 s

Diameter of the circle, D = 1. 9 m

The radius of the circle is the half of the diameter. So,

$r=\frac{D}{2}=\frac{1.9}{2}=0.95 \mathrm{m}$

One revolution is equal to 360 degree or 2 pi or 6.28 radians. Average speed is the ratio of total distance to the time. It can be expressed as

$\text {average speed, } v_{a v}=\frac{\text {total distance}}{\text {total time}}=\frac{2 \times \pi \times r}{1}$

$2 \times \pi \times r$ – The distance reached by the thrower to make one revolution

$v_{a v}=2 \times 3.14 \times 0.95=5.966 \mathrm{m} / \mathrm{s}$

Now, we need to the final velocity (speed of the discus at release). This can be done as below

$v_{a v}=\frac{1}{2} \times\left(v_{i}+v_{f}\right)$

By taking the average of combining both initial and final velocity, we get average velocity. Here, initial velocity is zero.

$5.966=\frac{1}{2} \times\left(0+v_{f}\right)$

$v_{f}=5.966 \times 2=11.932 \mathrm{m} / \mathrm{s}$

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Proton: Its electrical charge is +1, its mass is 1, it's found in the nucleus

Neutron: Its electrical charge is 0, its mass is 1, it's found in the nucleus

Electron: Its electrical charge is -1, its mass is negligible, it's found outside the nucleus

Explanation:

Atoms consist of three types of particles:

Proton: the proton is found in the nucleus of the atom, and it has a positive electric charge, equal to $+1.6\cdot 10^{-19}C$ (expressed in units of fundamental charge, it has a charge of +1). Its mass is $1.67\cdot 10^{-27}kg$ , while its mass expressed in atomic mass units is 1 a.m.u
Neutron: the neutron is also found in the nucleus of the atom, and it has no electric charge. Its mass is similar to the mass of the proton (slightly larger), and neutrons and protons are held together in the nucleus by the presence of the strong nuclear force
Electron: the electron orbits around the nucleus, far away from it. It has negative electric charge, opposite to that of the proton ( $-1.6\cdot 10^{-19}C$ , or -1 in units of fundamental charge). Its mass is much lower than that of the proton, approximately 1800 times smaller, so it can be considered as negligible.

Learn more about atoms:

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