The person pushes the trolley and suitcases across a horizontal surface at a steady speed of $1.4\,\text{m s}^{-1}$ and then lets go of the trolley. The trolley then travels in a straight line and eventually comes to rest. Assume that a constant total resistive force of $18\,\text{N}$ acts against the motion of the trolley and suitcases.
Calculate the power needed to overcome the total resistive force on the trolley and suitcases when they travel at a constant speed of $1.4\,\text{m s}^{-1}$.
Calculate the time for the trolley to come to rest after it has been released.
At a different location in the airport, the trolley and suitcases are on a slope, as shown in Fig. 2.1. The person lets the trolley go from rest at point $X$. The trolley travels down the slope in a straight line towards point $Y$. The distance along the slope from $X$ to $Y$ is $9.5\,\text{m}$. The component $F$ of the weight of the trolley and suitcases acting along the slope is $54\,\text{N}$. Assume that a constant total resistive force of $18\,\text{N}$ acts against the motion of the trolley and suitcases.
Calculate the speed of the trolley at point $Y$.
Calculate the work done by $F$ as the trolley moves from $X$ to $Y$.
The trolley is released from point $X$ at time $t = 0$. On Fig. 2.2, sketch a graph to show how the work done by $F$ varies with time $t$ for the trolley’s motion from $X$ to $Y$. Numerical values for the work done and for $t$ are not required.
The slope angle in (b) is constant. The frictional forces acting on the wheels of the moving trolley are also constant. Explain why, in practice, it is wrong to assume that the total resistive force opposing the motion of the trolley and suitcases remains constant as the trolley moves between $X$ and $Y$.
Calculate the speed of the trolley at point Y.
Calculate the work done by $F$ as the trolley moves from X to Y.
The trolley is released from point X at time $t = 0$. On Fig. 2.2, sketch a graph to show how the work done by $F$ varies with time $t$ for the trolley’s motion from X to Y. Numerical values of the work done $E$ are not required.