Work and energy

A child pulls a small cart for $5.0\mathrm{m}$ along a horizontal sidewalk with a rope that forms an angle of $40^{\circ }$ with the horizontal. The tension in the rope is constant and equal to $60\mathrm{N}$. Compute the work done by the tension.

Solution available to those who have unlocked the subject.

A block of mass $5.0\mathrm{kg}$ starts from rest and slides for $2.0\mathrm{m}$ down a smooth plane inclined at $30^{\circ }$. Compute the work done by the weight, the work done by the normal force and the final speed of the block.

Solution available to those who have unlocked the subject.

A spring with spring constant $k=250N/m$ is stretched from $4.0\mathrm{cm}$ to $12\mathrm{cm}$ beyond its rest length. Compute the work done by the elastic force during the stretching.

Solution available to those who have unlocked the subject.

A body moves along the $x$-axis from $x=0$ to $x=4.0\mathrm{m}$ under the action of a force with component $F_x(x)=2.0+1.5x$, where $x$ is in meters and $F_x$ in newtons. Compute the work done by the force.

Solution available to those who have unlocked the subject.

A body of mass $800\mathrm{g}$ goes from a speed of $2.0m/s$ to a speed of $6.0m/s$. Compute the total work done by the forces acting on it.

Solution available to those who have unlocked the subject.

A car travels at $90km/h$ on a horizontal road and brakes with locked wheels. The coefficient of kinetic friction between tires and asphalt is $0.70$. Compute the braking distance.

Solution available to those who have unlocked the subject.

A ball is thrown vertically upward with speed $12m/s$ from a point located $1.5\mathrm{m}$ above the ground. Neglecting air resistance, compute the maximum height reached by the ball, measured from the ground.

Solution available to those who have unlocked the subject.

A simple pendulum has an inextensible string of negligible mass and length $0.80\mathrm{m}$. Compute the minimum speed the ball must have at the lowest point for the string to reach the horizontal position.

Solution available to those who have unlocked the subject.

A block of mass $0.25\mathrm{kg}$ rests against a spring of constant $k=400N/m$ compressed by $5.0\mathrm{cm}$, on a smooth horizontal plane. Once the spring is released, the block moves up a smooth ramp. Compute the speed of the block after it leaves the spring and the maximum height it reaches on the ramp.

Solution available to those who have unlocked the subject.

A package of mass $2.0\mathrm{kg}$ starts from rest at the top of a slide $3.0\mathrm{m}$ high and reaches the bottom with speed $6.0m/s$. Compute the mechanical energy dissipated by friction.

Solution available to those who have unlocked the subject.

A block starts from rest at the top of a plane inclined at $30^{\circ }$ and slides along it for $2.0\mathrm{m}$. The coefficient of kinetic friction is $0.30$. Compute the speed of the block at the base of the plane.

Solution available to those who have unlocked the subject.

A cyclist, with a total mass including the bicycle of $80\mathrm{kg}$, climbs at constant speed $4.0m/s$ along a road inclined at $6.0^{\circ }$. Neglecting friction and air resistance, compute the power the cyclist must develop.

Solution available to those who have unlocked the subject.

A particle moves along the $x$-axis subject only to a conservative force with potential energy $U(x)=3x^2-x^3$, where $x$ is in meters and $U$ in joules. Determine the equilibrium positions and their stability, and determine for which values of the mechanical energy a particle located near $x=0$ stays confined to a bounded interval.

Solution available to those who have unlocked the subject.