Question

question 3
a ball at rest hangs from a single rope attached to the ceiling and does not touch the ground.
a student measures the tension force exerted on the ball by the rope to be equal to 686
newtons. what must be the mass of the ball in kilograms?

70 kg
686 kg
9.8 kg
6722.8 kg

Explanation:

Step1: Recall the formula for weight

The weight \( W \) of an object is given by \( W = mg \), where \( m \) is the mass and \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)). When the ball is at rest, the tension \( T \) in the rope equals the weight \( W \), so \( T = mg \).

Step2: Solve for mass \( m \)

We know \( T = 686 \, \text{N} \) and \( g = 9.8 \, \text{m/s}^2 \). Rearranging the formula \( m=\frac{T}{g} \).
Substitute the values: \( m = \frac{686}{9.8} \).
Calculate: \( \frac{686}{9.8}=70 \).

Answer:

70 kg