William Tell shoots an apple from his son's head. The speed of the 102-g arrow just before it strikes the apple is 26.7 m/s, and
1 answer:
To develop the problem, we require the values concerning the conservation of momentum, specifically as given for collisions.
By definition the conservation of momentum tells us that,
To find the speed at which the arrow impacts the apple we turn to the equation of time, in which,
The linear velocity of an object is given by
Replacing the equation of time we have to,
Velocity two is neglected since there is no velocity of said target before the collision, thus,
Clearing for m_2
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Answer:
The charge q₃ must be placed at X = +2.5 cm
Explanation:
Conceptual analysis
The electric field at a point P due to a point charge is calculated as follows:
E = k*q/d²
E: Electric field in N/C
q: charge in Newtons (N)
k: electric constant in N*m²/C²
d: distance from charge q to point P in meters (m)
The electric field at a point P due to several point charges is the vector sum of the electric field due to individual charges.
Equivalences
1µC= 10⁻6 C
1cm= 10⁻² m
Data
k = 8.99*10⁹ N×m²/C²
q₁ =+3 µC =3*10⁻⁶ C
q₂ = -10 µC =-10*10⁻⁶ C
q₃= +6µC =+6*10⁻⁶ C
d₁ = 3cm =3×10⁻² m
d₂ = 4cm = 4×10⁻² m
Graphic attached
The attached graph shows the field due to the charges:
E₁:Field at point P due to charge q₁. As the charge is positive ,the field leaves the charge. The direction of E1 is (+ x).
E₂: Field at point P due to charge q₂. As the charge is positive ,the field leaves the charge. The direction of E1 is (+ x).
Problem development
E₃: Field at point P due to charge q₃. As the charge q₃ is positive, the field leaves the charge.
The direction of E₃ must be (- x) so that the electric field can be equal to zero at point P since E₁ and E₂ are positive, then, q₃must be located to the right of point P.
We make the algebraic sum of fields at point P due to the charges q1, q2, and q3:
E₁+E₂-E₃=0
We eliminate k
We replace data
we eliminate 10⁻⁶
The charge q₃ must be placed at X = +2.5 cm
Given :
Distance of point P from the origin is , d = 9.83 mm .
To Find :
The electric field produced by this charge at point P , if charge is placed at origin .
Solution :
Let , charge on origin is q .
Electric field at point P is given by :
..... ( 1 )
Here , k is constant , .
Putting value of k and r in above equation , we get :
Hence , this is the required solution .