Question

what is the greatest mass of groceries that can be lifted safely with this bag given that the bag is raised with an acceleration of 1.80 m/s^2

Answer 1

The maximum safe mass of groceries that can be lifted with the bag, given a force of 52.0 N and an acceleration of 1.80 m/s^2, is approximately 28.9 kg. Exceeding this limit risks tearing the handles.

To determine the maximum mass of groceries that can be safely lifted with the bag, we can apply Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a). In this case, the force is the tension in the paper handles, and the acceleration is the upward acceleration of the bag.

The maximum force that can be applied without tearing the handles is given as 52.0 N. Using Newton's second law, we rearrange the formula to solve for mass (m = F/a). Plugging in the values, we find that the maximum mass (m) is equal to the force (52.0 N) divided by the acceleration (1.80 m/s^2), resulting in a maximum mass of approximately 28.9 kg.

Therefore, the greatest mass of groceries that can be lifted safely with this bag, considering the specified conditions, is approximately 28.9 kilograms. It's crucial to stay within this limit to prevent the handles from tearing off due to the applied force and acceleration.

Answer 2

We will have the following:

According to the image:

First, we remember that:

`F=m\cdot a`

Now, we will determine he maximum mass will be:

`52.0N=m\cdot(1.8m/s^2)\Rightarrow m=\frac{^{}52.0N}{1.80m/s^2}`
`\Rightarrow m=(260)/(9)kg\Rightarrow m\approx28.9kg`

So, the maximum mass will be approximately 28.9 kg.