Question

Consider the baby being weighed in Figure 4.34.

(a) What is the mass of the child and basket if a scale reading of 55 N is observed?

(b) What is the tension T1 in the cord attaching the baby to the scale?

(c) What is the tension T2 in the cord attaching the scale to the ceiling, if the scale has a mass of 0.500 kg?

(d) Draw a sketch of the situation indicating the system of interest used to solve each part. The masses of the cords are negligible.

Short answer

(a) The mass of the child and basket is 5.6 kg.

(b) The tension T₁ in the cord is 55 N.

(c)The tension T₂ in the cord is 59.9 N.

Step-by-step solution

Theory

Apply the following relation.

\(W = mg\)

Here, W is the weight of the child and basket, m is the mass of the child and basket, and g is the acceleration due to gravity.

(a) Determine the mass of the child and basket

Substitute 55N for W and 9.8 m/s² for g in the above expression, and we get,

\(\begin{array}{c}55\;{\rm{N}} = m \times 9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}\\m = \frac{{55\;{\rm{N}}}}{{9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}}}\\m = 5.6\;{\rm{kg}}\end{array}\)

Hence, the mass of the child and basket is 5.6 kg.

(b) Determine the tension T1 in the cord

Referring to the figure, the tension T₁ will be equal to the weight of the child and basket.

Therefore, T₁=55 N.

(c) Determine the tension T2 in the cord

Referring to the figure, the tension T2 will be equal to the weight of the weighing scale along with the weight of the child and basket.

\({T_2} = W + {m_w}g\)

Here, T2 is the tension in the cord connecting the weighing scale and the ceiling, and m₁ is the mass of the weighing scale.

Substitute 55 N for W, 0.5 kg for m₁, and 9.8m/s² for g.

\(\begin{array}{c}{T_2} = 55\;{\rm{N}} + 0.5\;{\rm{kg}} \times 9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}\\ = 55\;{\rm{N}} + 4.9\;{\rm{kg}} \cdot {\rm{m/}}{{\rm{s}}^{\rm{2}}}\\ = \left( {55 + 4.9} \right)\;{\rm{N}}\\ = 59.9\;{\rm{N}}\end{array}\)

Hence, the tension T2 in the cord is 59.9 N.

(d) The sketch of the system of interest.