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question:At a given instant, a particle with a mass of 5.00 milligrams and a charge of 3.70 nanoCoulombs has a velocity with a magnitude of 150,000 m/s in the positive y-direction. It moves in a uniform magnetic field of 0.800 Tesla, oriented in the negative x-direction. Part A) Determine the direction of the magnetic force acting on the particle. Part B) Calculate the magnitude of the magnetic force on the particle.
answer:The magnetic force (F) on a moving charged particle with charge (q) is given by the cross product: [ vec{F} = qvec{v} times vec{B} ] where ( vec{v} ) is the velocity vector of the particle, and ( vec{B} ) is the magnetic field vector. The direction of the force is determined using the right-hand rule. a.) For the positively charged particle moving along the positive y-axis in a magnetic field in the negative x-axis direction, the direction of the force can be found by the cross product: [ +y times +x = -z ] So, the magnetic force acts in the negative z-direction. b.) The magnitude of the force is calculated as: [ F = qvBsinphi ] where ( phi ) is the angle between the particle's velocity and the magnetic field. Since the angle between the velocity and magnetic field vectors is ( 90^circ ): [ F = (3.70 times 10^{-8}, text{C})(1.50 times 10^5, text{m/s})(0.800, text{T})sin(90^circ) ] [ F = 0.0044, text{N} ] Thus, the magnitude of the magnetic force on the particle is 4.4 milliNewtons.
question:What are the reactants and products in the balanced chemical equation for the preparation of chlorine?
answer:Reactants: Potassium permanganate (KMnO4) and hydrochloric acid (HCl) Products: Manganese(II) chloride (MnCl2), potassium chloride (KCl), water (H2O), and chlorine gas (Cl2)
question:Factor the number 63873 into its prime factors.
answer:To factor 63873 into its prime factors, we can start by finding the smallest prime number that divides it. We can see that 3 is the smallest prime number that divides 63873, so we can write: 63873 = 3 cdot 21291 Now, we can repeat this process with 21291. We can see that 47 is the smallest prime number that divides 21291, so we can write: 21291 = 47 cdot 453 Finally, we can see that 151 is the smallest prime number that divides 453, so we can write: 453 = 151 cdot 3 Therefore, the prime factorization of 63873 is 3^2cdot 47^1cdot 151^1. The answer is 3^2cdot 47^1cdot 151^1
question:Express the decimal 0.85 as a simplified fraction.
answer:The first decimal place after the point represents 'tenths' and the second decimal place represents 'hundredths'. #0.85 = 85/100# This simplifies to #17/20# The answer is #0.85 = 85/100 = 17/20#