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 2.15-kg container of potato salad at one end and a 0.750-kg package of hot dogs at the other end of a 52.0-cm long basket. Determine where she should place a 2.05-kg container of lemonade so that the basket balances at its center.

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 2.15-kg container of potato salad at one end and a 0.750-kg package of hot dogs at the other end of a 52.0-cm long basket. Determine where she should place a 2.05-kg container of lemonade so that the basket balances at its center.

Answer 1

To determine where Alice should place the container of lemonade so that the picnic basket balances at its center, we need to find the distance from the handle to the container of lemonade.

We can use the principle of moments to solve this problem. According to the principle of moments, the sum of the clockwise moments is equal to the sum of the counterclockwise moments.

First, let's assign a positive direction to the counterclockwise moments and a negative direction to the clockwise moments.

The moment of an object can be calculated by multiplying its mass by its distance from the reference point (in this case, the handle of the basket).

So, the clockwise moment caused by the container of potato salad can be calculated as follows:

Clockwise moment = (-mass of potato salad) * (distance from handle to potato salad)
= (-2.15 kg) * (52.0 cm)
= -111.8 kg·cm

Similarly, the clockwise moment caused by the package of hot dogs can be calculated as follows:

Clockwise moment = (-mass of hot dogs) * (distance from handle to hot dogs)
= (-0.750 kg) * (52.0 cm)
= -39.0 kg·cm

Now, let's find the counterclockwise moment that needs to be balanced by the container of lemonade.

Counterclockwise moment = (mass of lemonade) * (distance from handle to lemonade)

We need the sum of the clockwise moments to equal the sum of the counterclockwise moments, so:

-111.8 kg·cm + (-39.0 kg·cm) = (2.05 kg) * (distance from handle to lemonade)

Simplifying the equation:

-150.8 kg·cm = (2.05 kg) * (distance from handle to lemonade)

Now, we can solve for the distance from the handle to the container of lemonade:

distance from handle to lemonade = -150.8 kg·cm / 2.05 kg
≈ -73.56 cm

Since the distance is negative, it means that Alice should place the container of lemonade 73.56 cm on the opposite side of the handle from the potato salad and the hot dogs. This would ensure that the picnic basket balances at its center.