Newton’s laws and forces

A body of mass $8.0\mathrm{kg}$, initially at rest, moves on a smooth horizontal surface and reaches a velocity of $6.0m/s$ in $3.0\mathrm{s}$. Assuming the net force is constant, compute its magnitude.

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A body of mass $12\mathrm{kg}$ hangs at rest from two symmetric ideal strings, each forming an angle of $45^{\circ }$ with the horizontal. Compute the tension of each string.

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A block starts from rest and slides down a smooth plane inclined at $20^{\circ }$. Compute the time it takes to travel $4.0\mathrm{m}$ along the plane.

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A coin rests on a book, which is slowly tilted. The coin starts to slide when the cover forms an angle of $27^{\circ }$ with the horizontal. Compute the coefficient of static friction between coin and cover.

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A crate of mass $50\mathrm{kg}$ is dragged across a horizontal floor by a horizontal force of $300\mathrm{N}$. The coefficient of kinetic friction is ${\mu }_d=0.40$. Compute the acceleration of the crate.

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A body of mass $10\mathrm{kg}$ must be pushed up a plane inclined at $30^{\circ }$ at constant velocity, with coefficient of kinetic friction ${\mu }_d=0.20$. Compute the magnitude of the required force, parallel to the plane.

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A body of mass $5.0\mathrm{kg}$ hangs from two equal springs, connected in parallel, each with spring constant $400N/m$. Compute the extension of the springs at equilibrium.

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An Atwood machine carries at the ends of the string two bodies of masses $2.5\mathrm{kg}$ and $1.5\mathrm{kg}$. String and pulley are ideal. Compute the tension of the string during the motion.

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A block of mass $4.0\mathrm{kg}$ on a smooth horizontal table is connected, by an ideal string that passes over an ideal pulley at the edge of the table, to a hanging body of mass $1.0\mathrm{kg}$. Compute the tension of the string during the motion.

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A curve of radius $120\mathrm{m}$ has its roadway inclined at $15^{\circ }$ toward the center. Compute the speed at which a car travels around it without needing lateral friction.

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A bucket full of water is swung in a vertical plane along a circle of radius $0.90\mathrm{m}$. Compute the minimum speed the bucket must have at the highest point for the water to stay in the bucket.

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A person of mass $60\mathrm{kg}$ stands on a scale in an elevator, which at a certain instant reads $540\mathrm{N}$. Compute the acceleration of the elevator, indicating its sense.

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A pendulum hangs from the ceiling of a railway car that accelerates on a straight horizontal track with constant acceleration $3.0m/{\mathrm{s}}^2$. Compute the angle that the string forms with the vertical when the pendulum is at rest relative to the car.

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