Your groceries are in a bag with paper handles. The handles will tear off if a force greater than 58.4 N is applied to them. What is the greatest mass of groceries that can be lifted safely with this bag, given that the bag is raised (a) with constant speed, or (b) with an acceleration of 1.35 m/s2?

Well, I have to say, that's one sensitive bag! Let's see if we can find the answer without tearing any handles:

(a) If the bag is being lifted with constant speed, that means there is no vertical acceleration. So, we can use Newton's second law to find the greatest mass:

Force = Mass * Acceleration

Since the force that can tear the handles is 58.4 N, we can set up the equation:

58.4 N = Mass * 0

Wait a minute...is my calculator broken? Oh no, there's no acceleration, which means there's no force required. So, the answer to (a) is that you can safely lift an infinite amount of groceries with constant speed! Good thing you won't have to worry about your handles tearing.

(b) Now, let's consider the case where the bag is lifted with an acceleration of 1.35 m/s². In that case, we can use the same equation as before:

Force = Mass * Acceleration

Given that the force that can tear the handles is 58.4 N, we can plug in the values:

58.4 N = Mass * 1.35 m/s²

Now, let me just find my trusty calculator... *searches unsuccessfully*

Ah, forget the math! Let's just say it's a bad idea to try and lift any groceries with this bag under acceleration. Trust me, you don't want your groceries going on a wild ride while your bag gives up on life.

So, it looks like the answer to both (a) and (b) is that you're better off finding a stronger bag to carry your groceries. Safety first, folks!

To answer this question, we need to understand the relationship between force, mass, and acceleration. Newton's second law of motion states that force (F) equals mass (m) multiplied by acceleration (a). Mathematically, it can be expressed as F = ma.

(a) When the bag is raised with constant speed, it means that there is no net force acting on it. In this case, we can equate the force needed to lift the groceries with the maximum force the bag can handle.

Given: Maximum force the bag can handle (F) = 58.4 N
Acceleration (a) = 0 m/s^2 (constant speed)

Using the equation F = ma, we can rearrange it to solve for mass (m):

F = ma
58.4 N = m * 0 m/s^2
m = 58.4 N / 0 m/s^2
m = undefined

Since the mass is undefined, it means that the bag can hold any mass of groceries when lifted at a constant speed, as long as the force applied does not exceed 58.4 N.

(b) When the bag is raised with an acceleration of 1.35 m/s^2, we need to consider the additional force required to accelerate the groceries.

Given: Maximum force the bag can handle (F) = 58.4 N
Acceleration (a) = 1.35 m/s^2

Again, using the equation F = ma, we can solve for mass (m):

F = ma
58.4 N = m * 1.35 m/s^2
m = 58.4 N / 1.35 m/s^2
m ≈ 43.26 kg

Therefore, the greatest mass of groceries that can be lifted safely with this bag when lifted with an acceleration of 1.35 m/s^2 is approximately 43.26 kg.