Chapter 3, Problem 47A

Here a stone is suspended at rest by a string.

a. Draw force vectors for all the forces that act on the stone,

b. Should your vectors have a zero resultant?

c. Why, or why not?

To determine

To Sketch: The force vectors for the forces acting on the stone.

Explanation of Solution

Consider a stone is suspended by a string.

Consider the mass of the stone is denoted by $m$ .

Consider the acceleration due to gravity of the Earth is denoted by $g$ .

The gravitation force of the Earth applies a gravitational pull on the suspended stone.

For the stone to be in rest, the tension $\left(T\right)$ in the string acts in the upward direction.

Show the forces acting on the stone as shown in the Figure below:

  

Refer the Figure.

The stone’s weight $\left(W\right)$ acts in the downward direction.

The tension $\left(T\right)$ in the string act in the upward direction

Hence, the sketch for the force vectors for the forces acting on the stone is shown.

Conclusion:

Thus, the sketch for the force vectors for the forces acting on the stone is shown.

To determine

Whether the force vectors should have zero resultant.

Answer to Problem 47A

The force vectors (stone weight and tension in the string) should have zero resultant.

Explanation of Solution

Refer Part (a).

The weight $\left(W\right)$ of the stone acts downward.

The tension $\left(T\right)$ in the string acts in upward direction.

For the stone in rest condition, the weight of the stone equals the tension in the string.

Conclusion:

Thus, the force vectors (stone weight and tension in the string) should have zero resultant.

To determine

The reason whether the force vectors should have zero resultant or not.

Answer to Problem 47A

The force vectors (stone weight and tension in the string) should have zero resultant as the stone is in rest condition.

Explanation of Solution

Refer Part (a) and Part (b).

The weight $\left(W\right)$ of the stone acts downward.

The tension $\left(T\right)$ in the string acts in upward direction.

For the stone in rest condition, the weight of the stone equals the tension in the string.

The resultant vector for these equal and opposite forces is zero.

Conclusion:

Thus, the force vectors (stone weight and tension in the string) should have zero resultant as the stone is in rest condition.