Question

Alice is going on a picnic and is aware that it will be easier to carry the picnic basket if it balances at the center where the handle is attached. She has placed a 1.65-kg container of potato salad at one end and a 0.675-kg package of hot dogs at the other end of a 52.0-cm long basket. Determine where she should place a 1.85-kg container of lemonade so that the basket balances at its center.

Answer 1

= 13.7m

Step-by-step explanation:

Balancing moment about mid point

the equation will be

`m_1x_1+m_2x_2+m_3x_3 = 0`

Given that

m₁ = 1.65kg

m₂ = 0.675kg

distance x = 52cm

`(1.65)((-0.52)/(2) )+(0.675)((0.52)/(2) )+(1.85)x_3\\\\(1.85)x_3= (1.65)((0.52)/(2) )+(0.675)((-0.52)/(2) )`

`x_3 = ((1.65)((-0.52)/(2) )+(o.675)((0.52)/(2) ))/(1.85) \\\\= 0.137cm`

x = 13.7m

13.7m from the mid point towards 1.85kg mass so that basket balance at its center.

Answer 2

Answer: 13.703cm from the center of the basket on the end holding the 0.675kg package of hot dog.

Step-by-step explanation:

The center of the basket is at point 26 cm from each end of the basket.

This is gotten from the evaluation;

52cm/2.

The principle of moments is very important in solving this problem,

"The algebraic sum of all clockwise moments must be equal to he algebraic sum of all anticlockwise moments"

The statement above is the principle of moments.

Now to the question,

Since the acceleration due to gravity is assumed to be equal for all of the masses,

By intuition, the basket would tilt downwards on the end which holds the 1.65kg container of potato salad.

Consequently, to balance the basket 1.85kg container of lemonade must be placed at a distance, x from the center of the basket along the length of the basket (on the end holding the 0.675 package of hot dog).

Therefore, Taking moments about the center of the basket,

(1.65kg×26cm)=(0.675kg×26cm)+(1.85cm×xcm)

Therefore from the expression above, x = 13.703cm from the center on the basket on the side which holds the 0.675kg package of hot dog.

PS: The knowledge of moments of forces is very important in understanding machines especially those which are used for measuring weights relative to other weights.