Consider a situation where you exert a force F on a crate of mass m, moving it at a speed v a distance d across a floor in a time interval t. The quantity 1/2 mv2 is
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This expression represents the kinetic energy (KE) of the crate, where \( m \) is the mass of the crate and \( v \) is its speed. Show more…
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A net horizontal force $F$ is applied to a box with mass $M$ that is on a horizontal, frictionless surface. The box is initially at rest and then moves in the direction of the force. After the box has moved a dis- tance $D,$ the work that the constant force has done on it is $W_{D}$ and the speed of the box is $V$. The equation $P=F v$ tells us that the instanta neous rate at which $F$ is doing work on the box depends on the speed of the box. (a) At the point in the motion of the box where the force has done half the total work, and so has done work $W_{D} / 2$ on the box that started from rest, in terms of $V$ what is the speed of the box? Is the speed at this point less than, equal to, or greater than half the final speed? (b) When the box has reached half its final speed, so its speed is $V / 2,$ how much work has been done on the box? Express your answer in terms of $W_{D}$. Is the amount of work done to produce this speed less than, equal to, or greater than half the work $W_{D}$ done for the full displacement $D ?$
A net horizontal force $\boldsymbol{F}$ is applied to a box with mass $M$ that is on a horizontal, frictionless surface. The box is initially at rest and then moves in the direction of the force. After the box has moved a distance $D$, the work that the constant force has done on it is $W_{D}$ and the speed of the box is $V$. The equation $P=F v$ tells us that the instantaneous rate at which $\overrightarrow{\boldsymbol{F}}$ is doing work on the box depends on the speed of the box. (a) At the point in the motion of the box where the force has done half the total work, and so has done work $W_{D} / 2$ on the box that started from rest, in terms of $V$ what is the speed of the box? Is the speed at this point less than, equal to, or greater than half the final speed? (b) When the box has reached half its final speed, so its speed is $V / 2$, how much work has been done on the box? Express your answer in terms of $W_{D}$. Is the amount of work done to produce this speed less than, equal to, or greater than half the work $W_{D}$ done for the full displacement $D ?$
You exert a force of a known magnitude F on a grocery cart of total mass m. The force you exert on the cart points at an angle below the horizontal. Part A: If the cart starts at rest, determine an expression for the speed of the cart after it travels a distance d. Ignore friction. Express your answer in terms of the variables F, m, d, and θ.
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