Explanation If the car moves with the minimum possible speed at the top of the loop, the downward force of gravitation on the car must cause the centripetal acceleration. Write the expression for the gravitational force. F g = m g (I) Here, F g is the gravitational force, m is the mass, g is the acceleration due to gravity. Write the expression for the centripetal force . F C = m v t o p 2 r (II) Here, F C is the centripetal force, v t o p is the velocity, r is the radius of the loop. Equate equation (I) and (II) to solve for v t o p . v t o p = g r (III) Write the expression for the work-energy theorem for the car starting from rest, being accelerated by the rail gun, and reaching height 2 r at the top of the loop-the-loop. K i + U g i + W = K f + U g f (IV) Here, K is the kinetic energy, U is the gravitational potential energy, W is the work done. Write the expression for the W . W = F Δ x (V) Here, F is the force, Δ x is the displacement. Write the expression for K f . K f = 1 2 m v t o p 2 (VI) Here, K f is the final kinetic energy. Write the expression for U g f . U g f = m g ( 2 r ) (VII) Here, U g f is the final gravitational potential energy. In this case, the car is starting from the rest and height is zero with respect to the reference. So the initial kinetic energy and the gravitational potential energy is zero. Use equation (V), (VI), (VII) in (IV) and it becomes, 0 + 0 + F Δ x = 1 2 m v t o p 2 + m g ( 2 r ) (VIII) Write the expression for F . F → = I L → × B → F = I L B sin θ (IX) Here, I is the current, L is the length, B is the magnetic field

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ISBN: 9781260486919

Author: GIAMBATTISTA

Publisher: MCG

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Magnetic Force

A magnetic force arises when a charged particle or a current-carrying conductor is placed in a magnetic field. It is created because of the movement of the charged particles.

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Chapter 19, Problem 123P

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The minimum current must flow in the rails to give the car enough kinetic energy to make it around the loop without losing contact with the track.

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Chapter 19, Problem 122P

Chapter 19, Problem 124P

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The minimum current must flow in the rails to give the car enough kinetic energy to make it around the loop without losing contact with the track.

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The minimum current must flow in the rails to give the car enough kinetic energy to make it around the loop without losing contact with the track.

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Chapter 19 Solutions