The maximum force a grocery sack can withstand and not rip is 250 N. Calculate the greatest acceleration 20 kg of groceries can be lifted from the floor to the table such that the sack does not break.
Well you know the force and mass.
So use this formula: F=ma.
F=250N
m=20kg
Just rearrange it and you will be able to get the maximum acceleration the sack can withstand before breaking.
lifted at constant velocity?
F=mg
lifted at a constant acceleration?
F=m(a+g) solve for a
To calculate the greatest acceleration, we need to use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration (F = ma).
Given:
Maximum force the grocery sack can withstand without ripping = 250 N
Mass of groceries = 20 kg
We need to find the greatest acceleration that can be applied to the groceries, so we rearrange the formula to solve for acceleration:
a = F / m
Substituting the given values into the formula:
a = 250 N / 20 kg
a ≈ 12.5 m/s²
Therefore, the greatest acceleration 20 kg of groceries can be lifted from the floor to the table without ripping the sack is approximately 12.5 m/s².
To calculate the greatest acceleration without breaking the grocery sack, we need to consider the force applied to the sack during the lifting process. We know that the maximum force the sack can withstand is 250 N and that the weight of the groceries is 20 kg.
Step 1: Calculate the weight of the groceries:
The weight of an object is given by the formula:
Weight = mass × acceleration due to gravity (g)
In this case, the mass of the groceries is 20 kg. The acceleration due to gravity is approximately 9.8 m/s². Therefore, the weight of the groceries is:
Weight = 20 kg × 9.8 m/s² = 196 N
Step 2: Calculate the net force acting on the sack during lifting:
The net force is the difference between the applied force (lifting force) and the weight of the object being lifted. In this case, we want to find the maximum acceleration, so the net force should be equal to the maximum force the sack can withstand.
Net force = Applied force - Weight
Given that the maximum force the sack can withstand is 250 N and the weight of the groceries is 196 N, we have:
250 N = Applied force - 196 N
Simplifying the equation:
Applied force = 250 N + 196 N
Applied force = 446 N
Step 3: Calculate the maximum acceleration:
Acceleration is given by the formula:
Acceleration = Force / mass
In this case, the force is the applied force and the mass is the mass of the groceries.
Acceleration = 446 N / 20 kg
Acceleration ≈ 22.3 m/s²
Therefore, the greatest acceleration you can lift 20 kg of groceries from the floor to the table without breaking the sack is approximately 22.3 m/s².