On a horizontal air track, a glider of mass m carries a Γ-shaped post. The post supports a small dense sphere, also of mass m , hanging just above the top of the glider on a cord of length L . The glider and sphere are initially at rest with the cord vertical. A constant horizontal force of magnitude F is applied to the glider, moving it through displacement x 1 ; then the force is removed. During the time interval when the force is applied, the sphere moves through a displacement with horizontal component x 2 . (a) Find the horizontal component of the velocity of the center of mass of the glider–sphere system when the force is removed. (b) After the force is removed, the glider continues to move on the track and the sphere swings back and forth, both without friction. Find an expression for the largest angle the cord makes with the vertical.
On a horizontal air track, a glider of mass m carries a Γ-shaped post. The post supports a small dense sphere, also of mass m , hanging just above the top of the glider on a cord of length L . The glider and sphere are initially at rest with the cord vertical. A constant horizontal force of magnitude F is applied to the glider, moving it through displacement x 1 ; then the force is removed. During the time interval when the force is applied, the sphere moves through a displacement with horizontal component x 2 . (a) Find the horizontal component of the velocity of the center of mass of the glider–sphere system when the force is removed. (b) After the force is removed, the glider continues to move on the track and the sphere swings back and forth, both without friction. Find an expression for the largest angle the cord makes with the vertical.
Solution Summary: The author calculates the horizontal velocity of the centre of mass of glider and sphere system.
On a horizontal air track, a glider of mass m carries a Γ-shaped post. The post supports a small dense sphere, also of mass m, hanging just above the top of the glider on a cord of length L. The glider and sphere are initially at rest with the cord vertical. A constant horizontal force of magnitude F is applied to the glider, moving it through displacement x1; then the force is removed. During the time interval when the force is applied, the sphere moves through a displacement with horizontal component x2. (a) Find the horizontal component of the velocity of the center of mass of the glider–sphere system when the force is removed. (b) After the force is removed, the glider continues to move on the track and the sphere swings back and forth, both without friction. Find an expression for the largest angle the cord makes with the vertical.
A particle of mass 1.15 kg is subject to a force that is always pointed towards the East but whose magnitude changes linearly with time t. The magnitude of the force is given as F = (6 N/s)t. Let the x-axis point towards the East.
(a) Determine the change in the velocity Δv, in meters per second, of the particle between t = 0 and t = 1.2 sec.
(b) Determine the change in x-coordinate Δx, in meters, of the particle between t = 0 and t = 1.2 if the initial velocity is 12.6 m/s, and points in the same direction as the force.
A 0.35 kg particle moves in an xy plane according to x(t) = - 17 + 1 t - 5 t3 and y(t) = 18 + 5 t - 10 t2, with x and y in meters and t in seconds. At t = 1.5 s, what are (a) the magnitude and (b) the angle (within (-180°, 180°] interval relative to the positive direction of the xaxis) of the net force on the particle, and (c) what is the angle of the particle's direction of travel?
A particle of mass 1.3 kg is subject to a force that is always pointed towards the East but whose magnitude changes linearly with time t. The magnitude of the force is given as F = 5t, and has units of newtons. Let the x-axis point towards the East.
a)Determine the change in the velocity Δv, in meters per second, of the particle between t = 0 and t = 1.4 sec.
b)
Chapter 9 Solutions
Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics)
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