Two bowling balls are rolling toward each other. One of the balls, ball A, is 12 kg traveling to the right at a velocity of 3 m/
s, while the other ball, ball B, is 4 kg traveling at a velocity of 1 m/s to the left. They collide with each other and ball A bounces back to the left at a velocity of 1.2 m/s. How much velocity does ball B now have traveling to the right?
1 answer:
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The expression of the magnetic force and solving the determinant allows to shorten the result for the value of the magnetic force are:
- In Cartesian form F = 2.46 i ^ - 0.605 j ^
- In the form of magnitude and direction F = 2.53 N and θ = 346.2º
Given parameters.
- Length of the wire on the z axis is: L = 25.0 cm = 0.25 m.
- The current i = 9.00 A in the positive direction of the z axis.
- The magnetic field B = (-0.242 i ^ - 0.985 j ^ -0.336 k ^ ) T
To find.
- Magnetic force.
The magnetic force on a wire carrying a current is the vector product of the direction of the current and the magnetic field.
F = i L x B
Where the bold letters indicate vectors, F is the force, i the current, L a vector pointing in the direction of the current and B the magnetic field.
The best way to find the force is to solve the determinant, in general, a vector (L) is written in the form of the module times a <em>unit vector</em>.
Let's calculate.
F = 2.5 (0.985 i ^ - 0.242 j ^)
F = ( 2.46 i ^ - 0.605 j^ ) N
To find the magnitude we use the Pythagorean theorem.
F =
F =
F = 2.53 N
Let's use trigonometry for the direction.
Tan θ ’=
θ'= tan⁻¹
θ'= tan⁻¹1 ( )
θ’= -13.8º
To measure this angle from the positive side of the x-axis counterclockwise.
θ = 360- θ'
θ = 360 - 13.8
θ = 346.2º
In conclusion using the expression of the magnetic force and solving the determinant we can shorten the result for the value of the force are:
- In Cartesian form F = 2.46 i ^ - 0.605 j ^
- In the form of magnitude and direction F = 2.53 N and θ = 346.2º
Learn more here: brainly.com/question/2630590
Complete Question:
Suppose , where A has the dimensions LT, B has dimensions L²T⁻¹, and C has dimensions LT². Then the exponents n and m have the values
Answer:
The value of n = ¹/₅
The value of m = ³/₅
Explanation:
Given dimensions;
A = LT
B = L²T⁻¹
C = LT²
The values of n and m are calculated as follows;
Answer:
2. Using a shorter string of length L ′ ≈ 0.25 meters
5. Using a shorter string of length L ′ ≈ 0.5 meters
Explanation:
The period of a pendulum is given by
where
L is the length of the pendulum
g is the acceleration due to gravity
We see from the formula that the period of the pendulum depends only on its length, not on its mass or its amplitude of ocillation. Therefore, the only alterations that can change the period of the pendulum are the ones where its length is changed.
Moreover, we notice that the period is proportional to the square of the length: this means that in order to decrease the period of the pendulum (the problem asks us which alterations will reduce the period of the pendulum from 2 s to 1 s), the length of the pendulum should also be reduced.
Therefore, the only alterations that will reduce the period of the pendulum are:
2. Using a shorter string of length L ′ ≈ 0.25 meters
5. Using a shorter string of length L ′ ≈ 0.5 meters