• How to calculate electric field force?

    I have a charge of 4 at position 4. And a charge of -1 at position 7. What position would an electron e have to be to experience no net force? I can crudely guess the position is 10 using: Let q₁ = 4, q₂ = -1, q₃ = -1 Then for no net force to be acting on q₃ the electron, q₁q₃ / (x+3)² = q₂q₃ / x² 4 / (x+3)² = 1 / x² x = 3. So position of the... show more
    I have a charge of 4 at position 4. And a charge of -1 at position 7. What position would an electron e have to be to experience no net force? I can crudely guess the position is 10 using: Let q₁ = 4, q₂ = -1, q₃ = -1 Then for no net force to be acting on q₃ the electron, q₁q₃ / (x+3)² = q₂q₃ / x² 4 / (x+3)² = 1 / x² x = 3. So position of the electron is 10. But how do I use F = qE to solve this better?
    1 answer · Physics · 7 days ago
  • Adding and subtracting vectors, parallelogram rule?

    The following two vectors are sides of a parallelogram. u = <-3,0> v = <-9,9> What is the length of the diagonals? Diagonals meaning from corner to corner. I know adding u + v gives me the purple diagonal. u + v = <-12,9> ||u + v|| = √((-12)² + (9)²) = √(225) = 15 1) Why does u - v produce the other diagonal, in orange? I... show more
    The following two vectors are sides of a parallelogram. u = <-3,0> v = <-9,9> What is the length of the diagonals? Diagonals meaning from corner to corner. I know adding u + v gives me the purple diagonal. u + v = <-12,9> ||u + v|| = √((-12)² + (9)²) = √(225) = 15 1) Why does u - v produce the other diagonal, in orange? I thought it would be the gray line way below the x axis. 2) Do all vectors start from the same starting point, in this case the origin? Is it possible to get vectors s and t?
    1 answer · Mathematics · 2 weeks ago
  • Transpose of a matrix?

    Let A be the 2x2 matrix = 1 -3 -2 4 and 2x1 vector x = 5 3 1) (Ax)ᵀ = ? 2) Aᵀxᵀ = ? Number 2 is not defined while number 1 is defined. Why is this? For numer 1, is (Ax)ᵀ not equal to Aᵀxᵀ ?
    Let A be the 2x2 matrix = 1 -3 -2 4 and 2x1 vector x = 5 3 1) (Ax)ᵀ = ? 2) Aᵀxᵀ = ? Number 2 is not defined while number 1 is defined. Why is this? For numer 1, is (Ax)ᵀ not equal to Aᵀxᵀ ?
    3 answers · Mathematics · 1 month ago
  • What is Phase Shift in simple harmonic motion? Angular Frequency?

    Knowing that the position of oscillation is x(t) = Acos(ωt + φ) or sometimes I see x(t) = Acos(ωt - φ) 1) Does phase shift compensate for where you start from the equilibrium point, or the amplitude, or the initial velocity? And is it plus or minus? 2) Is ω angular frequency in simple harmonic motion related to ω angular velocity in uniform... show more
    Knowing that the position of oscillation is x(t) = Acos(ωt + φ) or sometimes I see x(t) = Acos(ωt - φ) 1) Does phase shift compensate for where you start from the equilibrium point, or the amplitude, or the initial velocity? And is it plus or minus? 2) Is ω angular frequency in simple harmonic motion related to ω angular velocity in uniform circular motion? I notice ω = 2π/T = 2πf in both cases :O Is it the "horizontal shadow" we see from circular motion to harmonic motion, if that makes sense?
    2 answers · Physics · 1 month ago
  • How to think of simple harmonic motion position equation?

    I know the equation x(t) = Acos((2π/T)t) How does this work? I know cosθ. It repeats every 2π radians. I know a block's motion repeats every T radians. And amplitude A is something like scaling everything together. But why is x(t) = Acos((2π/T)t) ? How does putting (2π/T) make everything work? I can't wrap my mind around 2π/T. What is... show more
    I know the equation x(t) = Acos((2π/T)t) How does this work? I know cosθ. It repeats every 2π radians. I know a block's motion repeats every T radians. And amplitude A is something like scaling everything together. But why is x(t) = Acos((2π/T)t) ? How does putting (2π/T) make everything work? I can't wrap my mind around 2π/T. What is going on?
    4 answers · Physics · 1 month ago
  • Angular kinematics, what is the direction of acceleration, torque, velocity?

    In the picture, the wheel is "accelerated up to operating speed". 1) Do I have things labelled correctly? 2) If the wheel were "slowing down by frictional torque", would angular acceleration be point backward then? 3) In the formula Torque T = Fr, is F the "frictional torque" spoken above? What direction would this... show more
    In the picture, the wheel is "accelerated up to operating speed". 1) Do I have things labelled correctly? 2) If the wheel were "slowing down by frictional torque", would angular acceleration be point backward then? 3) In the formula Torque T = Fr, is F the "frictional torque" spoken above? What direction would this force be? Just trying to see where everything is, I actually can't find any clear images of which way everything is pointed :( And I need visuals to learn :(
    1 answer · Physics · 1 month ago
  • Given spring constant and compression, find speed of launch?

    A spring has a restoring force given by\ F = -kx³ The spring, with k = 200 N/m³ is compressed 0.1 m. A 2kg mass is launched horizontally. What is the speed after launch? I know elastic force is governed by F = (1/2)kx². I was thinking of finding the derivative. Instead, you are suppose to find the integral?? Why in the world is this? Making... show more
    A spring has a restoring force given by\ F = -kx³ The spring, with k = 200 N/m³ is compressed 0.1 m. A 2kg mass is launched horizontally. What is the speed after launch? I know elastic force is governed by F = (1/2)kx². I was thinking of finding the derivative. Instead, you are suppose to find the integral?? Why in the world is this? Making zero sense :(
    2 answers · Physics · 1 month ago
  • Force required to stop spinning disc? Coefficient of friction wtf?

    A disc of radius 1.5m is initially spinning. It is stopped by a torque of -785.3 Nm, I calculate. The coefficient of friction is 0.60. What is the force needed to stop the disc? Torque = Force x Radius T = Fr F = T/r F = -785.3 Nm / 1.5 m = -524 N. Stopping force is 524 N / 0.60 = -872 N. ***Why do I now divide by coefficient of friction? This... show more
    A disc of radius 1.5m is initially spinning. It is stopped by a torque of -785.3 Nm, I calculate. The coefficient of friction is 0.60. What is the force needed to stop the disc? Torque = Force x Radius T = Fr F = T/r F = -785.3 Nm / 1.5 m = -524 N. Stopping force is 524 N / 0.60 = -872 N. ***Why do I now divide by coefficient of friction? This is this one part I've been stumped on for the last hour :( ***Why do I divide by the coefficient of friction just like that? No need for F = μN or anything, it just seems so random to divide at the end!
    2 answers · Physics · 1 month ago
  • Calculate effective spring constant? Why is it negative?

    I put 105 kg on a vertical spring. It stretches down 0.0065 m. Effective spring constant? In this instant I know there is gravitational force down, Fg = mg. Taken place is displacement of the spring downward. Spring force opposes displacement, so it is upward. Since the stretched spring is held stretched, net force is 0. So gravitational force... show more
    I put 105 kg on a vertical spring. It stretches down 0.0065 m. Effective spring constant? In this instant I know there is gravitational force down, Fg = mg. Taken place is displacement of the spring downward. Spring force opposes displacement, so it is upward. Since the stretched spring is held stretched, net force is 0. So gravitational force equals elastic force. Thus Fg = Fe. Fg = mg. Fe = -kΔx. Now, my problem is my signs. So up is positive, down is negative. mg = -kΔx (105 kg)(-9.81 ms⁻²) = -k(-0.0065 m - 0 m) -1030.05 kgms⁻² = -k(-0.0065 m) 158,469 = -k k = -158,469 N/m ? 1) What is the negative sign in F = -kx ? It is really confusing me! 2) And what is "effective" spring constant?
    1 answer · Physics · 1 month ago
  • Calculate acceleration due to gravity on satellite?

    Say a skateboard is on a U shaped ramp. At the maximum height, potential energy is maximum. At the bottom centre, kinetic energy is maximum. So E = PE + KE always. You're juggling PE and KE. 1) What force are involved in a satellite around earth? Just curious. Is potential energy just fixed? E = PE + ? + ?... What energies are you... show more
    Say a skateboard is on a U shaped ramp. At the maximum height, potential energy is maximum. At the bottom centre, kinetic energy is maximum. So E = PE + KE always. You're juggling PE and KE. 1) What force are involved in a satellite around earth? Just curious. Is potential energy just fixed? E = PE + ? + ?... What energies are you juggling? 2) A satellite is 275,000 m above earth. What is acceleration due to gravity on the satellite? a = Gm/r² a = (6.67E-11 Nm²kg⁻²)(5.972E24 kg)/(6,371,000 m + 275,000 m)² a = 0.92 ms⁻² *** Why do I consider the largest mass body always, in this case earth? I don't understand how we can somehow just neglect the mass of the satellite magically :O
    2 answers · Physics · 1 month ago
  • What is moment of inertia, torque, perpendicular level arm?

    Kicking a ball, I produce an angular acceleration of α = 27.5 rad/s^2 The moment of inertia of my lower leg is 0.55 kgm^2. The muscle the generates the kick is above the knee. It has an "effective perpendicular level arm of 1.75 cm". What is the force of the kick? α = 27.5 rad/s^2 I = 0.55 kgm^2 r = 0.0175 m F = Iα / r = (0.55)(27.5) /... show more
    Kicking a ball, I produce an angular acceleration of α = 27.5 rad/s^2 The moment of inertia of my lower leg is 0.55 kgm^2. The muscle the generates the kick is above the knee. It has an "effective perpendicular level arm of 1.75 cm". What is the force of the kick? α = 27.5 rad/s^2 I = 0.55 kgm^2 r = 0.0175 m F = Iα / r = (0.55)(27.5) / (0.0175) = 864.3 N. This is correct. But I am having trouble understanding knowing what each variable is. I realize the formula Fr = τ = Iα, Force * radius = Torque = Inertia * acceleration. 1) Have I labelled everything correctly? Sometimes torque is given by τ = Frsinθ and other times I see τ = Fr 2) Which is correct? I couldn't solve this problem for the longest time because I thought I needed to find the angular displacement. 3) What is a "perpendicular lever arm"? :(
    1 answer · Physics · 1 month ago
  • Moving a box, how is there an equal and opposite reaction?

    I push a box horizontally. My hands push against the box with force F. The box accelerates forward. How is it that the box is pushing back on my hand with force F? Yet for there to be acceleration, or change in velocity, there is an unbalanced force. With every action there is an equal and opposite reaction. Where is the reaction force? I've... show more
    I push a box horizontally. My hands push against the box with force F. The box accelerates forward. How is it that the box is pushing back on my hand with force F? Yet for there to be acceleration, or change in velocity, there is an unbalanced force. With every action there is an equal and opposite reaction. Where is the reaction force? I've read its me pushing backward on the earth and friction of the box? I still don't find this intuitive :( Help :(
    2 answers · Physics · 1 month ago
  • Direction of centripetal acceleration?

    Do I have everything pointed in the correct direction? *Is centripetal acceleration always pointing from the mass to the center? *Is centripetal acceleration = angular acceleration? Just two names for one thing? It's confusing :(
    Do I have everything pointed in the correct direction? *Is centripetal acceleration always pointing from the mass to the center? *Is centripetal acceleration = angular acceleration? Just two names for one thing? It's confusing :(
    1 answer · Physics · 1 month ago
  • Direction of centripetal acceleration and tension force?

    Do I have everything pointed in the correct direction? *Is centripetal acceleration always pointing from the mass to the center? *Why does tension seem to point in the opposite direction? If I have a mass hanging down from the ceiling, tension force is up! But I would think tension is down, as the mass is pulling down on the string right? :( Thanks!
    Do I have everything pointed in the correct direction? *Is centripetal acceleration always pointing from the mass to the center? *Why does tension seem to point in the opposite direction? If I have a mass hanging down from the ceiling, tension force is up! But I would think tension is down, as the mass is pulling down on the string right? :( Thanks!
    1 answer · Physics · 2 months ago
  • Columns of a matrix are linearly independence if only the trivial solution exists?

    "The columns of matrix A are linearly independent if and only if the equation Ax = 0 has only the trivial solution". A is a matrix. x is a vector. 0 is a zero vector. Why is this true? I know linear independence means each vector is "pointing" in a unique direction. But why does a trivial solution mean this is so? :(
    "The columns of matrix A are linearly independent if and only if the equation Ax = 0 has only the trivial solution". A is a matrix. x is a vector. 0 is a zero vector. Why is this true? I know linear independence means each vector is "pointing" in a unique direction. But why does a trivial solution mean this is so? :(
    2 answers · Mathematics · 2 months ago
  • Help with basis vector, vector length notation and terminology?

    Say I have the vector v = [-3, 4, 1, -4] Is the notation for the length/norm of a vector v given by: ||v|| ? so ||v|| = √(-3)² + (4)² + (1)² + (-4)² = √(42) And if I divide vector v by ||v|| I get the vector [-3/√(42), 4/√(42), 1/√(42), -4/√(42)] ***What is this vector and what is it called? A basis vector?
    Say I have the vector v = [-3, 4, 1, -4] Is the notation for the length/norm of a vector v given by: ||v|| ? so ||v|| = √(-3)² + (4)² + (1)² + (-4)² = √(42) And if I divide vector v by ||v|| I get the vector [-3/√(42), 4/√(42), 1/√(42), -4/√(42)] ***What is this vector and what is it called? A basis vector?
    3 answers · Mathematics · 2 months ago
  • How to multiply a vector and a matrix?

    Say I have a vector in 2 dimensional space, x = [2. 4] And a matrix, A = 2 3 1 5 1 4 Then Ax = [24 10 18]. This vector, b, is in 3 dimensional space. These are called transformations in linear algebra. So A transforms x into b. Is there anyway/anything I can do to visualise this? Here I know matrix A, but my level of understanding would be the... show more
    Say I have a vector in 2 dimensional space, x = [2. 4] And a matrix, A = 2 3 1 5 1 4 Then Ax = [24 10 18]. This vector, b, is in 3 dimensional space. These are called transformations in linear algebra. So A transforms x into b. Is there anyway/anything I can do to visualise this? Here I know matrix A, but my level of understanding would be the same as if matrix A was an unknown thing/blob/poop to me. What did matrix A do to the vector x?
    1 answer · Mathematics · 2 months ago
  • How to find the eigenvalues and eigenvectors of a 2x2 matrix?

    A = -5 6 -9 10 I know "characteristic polynomial" (I have no idea what this means) is P(λ) = Determinant of the matrix [-5-λ 6; -9 10-λ] P(λ) = (-5-λ)(10-λ) - (6)(9) P(λ) = -50 + 5λ - 10λ + λ² + 54 P(λ) = λ² - 5λ + 4 P(λ) = (λ - 4)(λ - 1) = 0 λ = 4, 1 = our eigenvalues. How do I find the eigenvectors for each eigenvalue? :O
    A = -5 6 -9 10 I know "characteristic polynomial" (I have no idea what this means) is P(λ) = Determinant of the matrix [-5-λ 6; -9 10-λ] P(λ) = (-5-λ)(10-λ) - (6)(9) P(λ) = -50 + 5λ - 10λ + λ² + 54 P(λ) = λ² - 5λ + 4 P(λ) = (λ - 4)(λ - 1) = 0 λ = 4, 1 = our eigenvalues. How do I find the eigenvectors for each eigenvalue? :O
    1 answer · Mathematics · 2 months ago
  • What is a determinant, in linear algebra?

    I've been looking for a simple description of what a determinant is to better my own understanding. But I guess it's very complicated? I'd like some input from others' knowledge on determinants :D As far as I understand it, the determinant is basically a "special/mysterious number" that tells us by what factor something... show more
    I've been looking for a simple description of what a determinant is to better my own understanding. But I guess it's very complicated? I'd like some input from others' knowledge on determinants :D As far as I understand it, the determinant is basically a "special/mysterious number" that tells us by what factor something grows by? https://www.youtube.com/watch?v=vvR3JSXO... In this short video, a determinant is basically by what factor volume grows!
    2 answers · Mathematics · 2 months ago
  • Can final momentum be greater than initial momentum?

    A stationary object is hit by a moving object. Can the stationary object have a final momentum larger than the initial momentum of the object that hits it? I vaguely remember something from my professor, yes if there is any rebound of something? I'm not sure though. Please help me with this concept!
    A stationary object is hit by a moving object. Can the stationary object have a final momentum larger than the initial momentum of the object that hits it? I vaguely remember something from my professor, yes if there is any rebound of something? I'm not sure though. Please help me with this concept!
    2 answers · Physics · 2 months ago