Chapter 3, Problem 48A

Here a stone is being accelerated vertically upward.

a. Draw force vectors to some suitable scale showing relative forces acting on the stone.

b. Which is the longer vector, and why?

To determine

To Draw: The force vectors to some suitable scale showing the relative forces acting on the stone

Explanation of Solution

W is the weight of the body which is acting downward

  $W=mg$

Where m is mass of the stone and g is gravitational acceleration

Tension on the string, acting as a upward force on the stone

The stone is moving with an acceleration a in upward direction, so the net upward force is F.

  $F=ma$

  $T-W=ma$

To determine

To Find: The longer vector among $\overrightarrow{T}$ and $\overrightarrow{W}$ .

Answer to Problem 48A

  $\overrightarrow{T}$ is the longer vector

Explanation of Solution

Arrow of a vector denotes the direction and length of the vector tells about the magnitude. Longer the vector, greater its magnitude is.

Although $\overrightarrow{W}$ acts downward, yet the stone moves upward with an acceleration $\overrightarrow{a}$ by the influence of $\overrightarrow{T}$ acting upwards.

So, it is clear that $\overrightarrow{T}$ >$\overrightarrow{W}$

So, the magnitude of the upward tension is greater than the magnitude of downward weight.

Hence, $\overrightarrow{T}$ is longer than $\overrightarrow{W}$ .