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LekaFEV [45]
3 years ago
14

In the first figure here, a sled is held on an inclined plane by a cord pulling directly up the plane. The sled is to be on the

verge of moving up the plane. In the second figure, the magnitude F required of the cord's force on the sled is plotted versus the coefficient of static friction μs between sled and plane: F1 = 2.2 N, F2 = 4.5 N, and μ2 = 0.512. At what angle θ (in ˚) is the plane inclined?
Physics
1 answer:
Charra [1.4K]3 years ago
4 0
When it says something like 'on the verge of moving,' it means that the pulling force and static friction force and gravitational force all cancel out! Any more pulling force and it is ready to move! At some point, you want F as a function of <span>μs</span>, to determine the force needed depending on the coefficient of static friction. This function, <span>F(<span>μs</span>)</span>, will rely on the angle θ as well, but we want to consider just one angle θ in every scenario. One value means it is constant. But if we know the F, and we know <span>μs</span>, we can find what the constant angle θ must be! If F is the pulling force, <span>FS</span> is the static friction force, and <span>FG</span> is gravitational force, <span><span><span>Fnet</span>=0</span><span>=F+<span>FS</span>+<span>FG</span></span><span>=F+<span>FN</span><span>μs</span>+mgsinθ</span><span>=F+mgcosθ<span>μs</span>+mgsinθ</span><span>=0</span></span> Then you can find <span>F(<span>μs</span>)</span>, but then there is the issue of solving for the θ<span> to make it true.</span>
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Answer:

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6 0
2 years ago
To understand how to find the velocities of objects after a collision.
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There are some information missing on Part D: Let the mass of object 1 be m and the mass of object 2 be 3m. If the collision is perfectly inelastic, what are the velocities of the two objects after the collision? Give the velocity v_1 of object one, followed by object v_2 of object two, separated by a comma. Express each velocity in terms of v.

Answer: Part A: v_1 = 0; v_2 = v

Part B: v_1 = v_2 = \frac{v}{2}

Part C: v_1 = \frac{v}{3}; v_2 = \frac{4v}{3}

Part D: v_1 = v_2 = \frac{v}{4}

Explanation: In elastic collisions, there no loss of kinetic energy and momentum is conserved. Momentum is determined as p = m.v and kinetic energy as K = \frac{1}{2}m.v^{2}

Conserved means that the amount of initial momentum is equal to the amount of final momentum:

m_{1}.v_{1i} + m_{2}.v_{2i} = m_{1}.v_{1f} + m_{2}.v_{2f}

No loss of energy means that initial kinietc energy is the same as the final kinetic energy:

\frac{1}{2}(m_{1}.v_{1i} + m_{2}.v_{2i}) = \frac{1}{2} (m_{1}.v_{1f} + m_{2}.v_{2f}  )

To determine the final velocities of each object, there are 2 variables and two equations, so working those equations, the result is:

v_{2f} = \frac{2.m_{1} } {m_{1} + m_{2} }.v_{1i}  + \frac{(m_{2} - m_{1})}{m_{1} + m_{2} } . v_{2i}

v_{1f} = \frac{m_{2} - m_{1} }{m_{1} + m_{2} } . v_{1i} + \frac{2.m_{2} }{m_{1} + m_{2} } .v_{2i}

For all the collisions, object 2 is static, i.e. v_{2i} = 0

<u>Part A</u>: Both objects have the same mass (m), v_{1i} = v and collision is elastic:

v_1 = \frac{m_{2} - m_{1}}{m_{1} + m_{2} } . v_{1i}

v_1 = 0

v_2 = \frac{2.m_{1} }{m_{1} + m_{2}}.v_{1i}

v_2 = \frac{2.m}{m+m}.v

v_2 = v

When the masses are the same and there is an object at rest, the object in movement stops and the object at rest has the same same velocity as the object who hit it.

<u>Part B</u>: Same mass but collision is inelastic: An inelastic collision means that after it happens, the two objects has the same final velocity, then:

m_{1}.v_{1i} + m_{2}.v_{2i} = m_{1}.v_{1f} + m_{2}.v_{2f}

m_{1}.v_{1i} = (m_{1}+m_{2}).v_{f}

v_{f} =  \frac{m_{1}.v_{1i}}{m_{1} + m_{2} }

v_1 = v_2 = \frac{m.v}{m+m}

v_1 = v_2 = \frac{v}{2}

<u>Part C:</u> Object 1 is 2m, object 2 is m and elastic collision:

v_1 = \frac{m_{2} - m_{1}}{m_{1} + m_{2} } . v_{1i}

v_1 = \frac{2m - m}{2m + m } . v

v_1 = \frac{v}{3}

v_2 = \frac{2.m_{1} }{m_{1} + m_{2}}.v_{1i}

v_2 = \frac{2.2m}{2m+m}.v

v_2 = \frac{4v}{3}

<u>Part D</u>: Object 1 is m, object is 3m and collision is inelastic:

v_1 = v_2 = v_{f} =  \frac{m_{1}.v_{1i}}{m_{1} + m_{2} }

v_1 = v_2 = \frac{m}{m+3m}.v

v_1 = v_2 = \frac{v}{4}

5 0
3 years ago
A radio wave transmits 38.5 W/m2 of power per unit area. A flat surface of area A is perpendicular to the direction of propagati
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Answer:

P=2.57\times 10^{-7}\ N/m^2

Explanation:

Given that,

A radio wave transmits 38.5 W/m² of power per unit area.

A flat surface of area A is perpendicular to the direction of propagation of the wave.

We need to find the radiation pressure on it. It is given by the formula as follows :

P=\dfrac{2I}{c}

Where

c is speed of light

Putting all the values, we get :

P=\dfrac{2\times 38.5}{3\times 10^8}\\\\=2.57\times 10^{-7}\ N/m^2

So, the radiation pressure is 2.57\times 10^{-7}\ N/m^2.

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