A gorgeous sack comes with a stand that holds a maximum of 230 N before it rips. Will a bag holding 15 kg of groceries that is lifted from the checkout counter at an acceleration o... A gorgeous sack comes with a stand that holds a maximum of 230 N before it rips. Will a bag holding 15 kg of groceries that is lifted from the checkout counter at an acceleration of 7.0 m/s² hold?
Understand the Problem
The question is asking whether a bag that can hold a maximum weight of 230 N can safely carry a load of groceries weighing 15 kg being lifted with an acceleration of 7.0 m/s². We will calculate the force exerted by the groceries when lifted to determine if it exceeds the bag's limit.
Answer
$F \approx 148.5 \, \text{N}$
Answer for screen readers
The total force exerted by the groceries when lifted is approximately $F \approx 148.5 , \text{N}$, which is within the bag's maximum limit of 230 N.
Steps to Solve
- Calculate the Weight of the Groceries
First, we need to calculate the weight of the groceries. The weight ($W$) can be found using the formula:
$$ W = m \cdot g $$
Where:
- $m$ is the mass (15 kg)
- $g$ is the acceleration due to gravity (approximately $9.81 , \text{m/s}^2$)
- Calculate the Total Force When Lifting
Next, we determine the total force ($F$) exerted by the groceries when they are lifted with an acceleration ($a$) of $7.0 , \text{m/s}^2$. This force can be calculated using Newton's second law:
$$ F = m \cdot (g + a) $$
Where:
- $a = 7.0 , \text{m/s}^2$
- Check Against the Bag's Maximum Weight Limit
Finally, we will determine if the force calculated in Step 2 exceeds the bag's maximum weight capacity of 230 N.
The total force exerted by the groceries when lifted is approximately $F \approx 148.5 , \text{N}$, which is within the bag's maximum limit of 230 N.
More Information
The total force exerted while lifting the groceries combines both the gravitational force and the additional force from the acceleration. Knowing the values for mass and acceleration allows us to ensure that the bag can safely carry the load without exceeding its limit.
Tips
- Forgetting to include the acceleration due to gravity when calculating the total force.
- Miscalculating the force by not correctly applying Newton's second law.
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