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Leona [35]
2 years ago
12

A small toy school bus rear-ends a big toy school bus initially at rest. The bigger bus is several times heavier than the smalle

r one. Which of the following statements are true if the collision is elastic?
True / False / Maybe.
1. The two busses continue together at the same speed.
2. Mechanical energy is conserved.
3. The small bus exerts the same amount of force on the big bus as vice versa.
4. Momentum is conserved.
5. The small bus will go backwards.
Physics
1 answer:
Mars2501 [29]2 years ago
4 0

Answer:

Explanation:

1 . The two busses continue together at the same speed.

FALSE STATEMENT .

The small bus will have twice the velocity of bigger bus  velocity in the same direction . The bigger bus will continue with the same velocity .

2. Mechanical energy is conserved

TRUE STATEMENT.

3  The small bus exerts the same amount of force on the big bus as vice versa.

TRUE STATEMENT.

4.Momentum is conserved

TRUE STATEMENT.

5.The small bus will go backwards

FALSE STATEMENT .

The small bus will have twice the velocity of bigger bus  velocity in the same direction .

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Statement :- We assume the orthagonal sequence {{\{\phi\}}_{1}^{\infty}} in Hilbert space, now {\forall \sf \:v\in \mathbb{V}}, the Fourier coefficients are given by:

{\quad \qquad \longrightarrow \sf a_{i}=(v,{\phi}_{i})}

Then Bessel's inequality give us:

{\boxed{\displaystyle \bf \sum_{1}^{\infty}\vert a_{i}\vert^{2}\leqslant \Vert v\Vert^{2}}}

Proof :- We assume the following equation is true

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So that, {\bf v_n} is projection of {\bf v} onto the surface by the first {\bf n} of the {\bf \phi_{i}} . For any event, {\sf (v-v_{n})\perp v_{n}}

Now, by Pythagoras theorem:

{:\implies \quad \sf \Vert v\Vert^{2}=\Vert v-v_{n}\Vert^{2}+\Vert v_{n}\Vert^{2}}

{:\implies \quad \displaystyle \sf ||v||^{2}=\Vert v-v_{n}\Vert^{2}+\sum_{i=1}^{n}\vert a_{i}\vert^{2}}

Now, we can deduce that from the above equation that;

{:\implies \quad \displaystyle \sf \sum_{i=1}^{n}\vert a_{i}  \vert^{2}\leqslant \Vert v\Vert^{2}}

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Answer:

|a|=2.83\ m/s^2

\theta=75^o

Explanation:

<u>Net Force And Acceleration </u>

The Newton's second law relates the net force applied on an object of mass m and the acceleration it aquires by

\vec F_n=m\vec a

The net force is the vector sum of all forces. In this problem, we are not given the magnitude of each force, only their angles. For the sake of solving the problem and giving a good guide on how to proceed with similar problems, we'll assume both forces have equal magnitudes of F=40 N

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The direction of the acceleration is the same as the net force:

\displaystyle tan\theta=\frac{54.64}{14.64}

\theta=75^o

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2 years ago
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