Question

You are taking care of two small children, Sarah and Rachel, who are twins. On a nice cool, clear day you decide to take them rollerblading. To travel down the smooth sidewalk you have Sarah hold your hand and Rachel's hand. The three of you form a straight line as you skate, and the two children just glide behind you. Sarah must reach up at an angle of 60 degrees to grasp your hand, but she grabs Rachel's hand horizontally. Since the children are twins, they are the same height and the same weight, 23 kg. To get started you accelerate at 2.0 m/s2 . You are concerned about the force on the children's arms, which might cause shoulder damage, so you calculate the force Sarah exerts on Rachel's arm, and the force you exert on Sarah's other arm. You assume that the frictional forces of the sidewalk on the rollerblades are negligible.

Answer 1

46N and 184N

Step-by-step explanation:

parameters given

angle of inclination of the force on sarah = 60⁰

mass of sarah = mass of rachel = 23kg

acceleration (equal for all the bodies) = 2.0m/s²

F is the force exerted on Sarah's arm

T is the tension between Sarah and Rachel

let the forces acting and the body diagram be represented as shown in the diagram below

the tension T exacted on rachel is given by

T = ma

hence

T = 23 × 2 = 46N

this is the force sarah exerts on Rachel

Now the Force exerted on Sarah's arm is given by

`Fcos60^(0) - T = ma`

where Fcos 60⁰ is the component of the force exerted on sarah's arm in the horizontal direction

now, T = 46N, mass of sarah, m = 23 kg and acceleration, a = 2m/s²

making F the subject of formula

`F = (ma + T)/(cos 60^(0) )`

`F = ((23 * 2) + 46 )/(cos 60^(0) )`

F = 184N

Answer 2

Step-by-step explanation:

Rachel and Sarah are standing on horizontal ground . Let T₁ be the tension between Rachel and Sarah and Sarah is in between you.

Force = mass x acceleration

Apply this equation on Rachel

T₁ = 23 x 2 = 46 N

Let T₂ be tension between Sarah and me and it is inclined at 60°

Force = mass x acceleration

Apply this equation on Sarah

T₂ cos 60 - T₁ = 23 X 2 = 46

T₂ cos 60 - 46 =46

T₂ cos 60 = 92

T₂ = 92 / .5

= 184 N