Your groceries are in a bag with paper handles. The handles will tear off if a force greater than 59 N is applied to them.

(a) What is the greatest mass of groceries that can be lifted safely with this bag, given that the bag is raised with constant speed? kg
(b) What if it is raised with an acceleration of 1.25 m/s2? kg

Well tiffany, you use this equasion: F=ma+mg. Manipulate the formula to get mass (which is the unknown here) on one side:

f= ma+mg
FACTOR m
f=m(a+g)
DIVIDE BOTH SIDES BY (a+g)
)=m

This can be used for both parts of the equasion. (remember that g=9.81 m/s^2.)

a)Since the bag is lifted with constant acceleration, "a" can be ignored. So:
f/g=m m=59/9.81= 6.01kg

b)for this part just don't ignore the acceleration. plug 1.25m/s into the formula.
m=) m=59/(1.25+9.81)= 5.33kg

(a) Well, it seems like this bag has a serious aversion to heavy lifting! To find the greatest mass of groceries that can be lifted safely with this bag, we first need to determine the force it can handle. Since we know that the handles will tear off if a force greater than 59 N is applied, we can use Newton's second law (F = m * a) to find the mass.

In this case, since the bag is raised with a constant speed, the acceleration (a) is zero. Therefore, we can rearrange the equation to solve for mass (m):

F = m * a
59 N = m * 0
m = 0 kg

Oops! Looks like this bag can't handle any mass at all if it's raised with a constant speed. You might want to reconsider using this bag if you're planning on buying groceries!

(b) Now, let's see what happens if the bag is raised with an acceleration of 1.25 m/s². We'll need to use the same equation as before, but this time we'll plug in the given acceleration:

F = m * a

Since the maximum force the handles can handle is still 59 N, we can rearrange the equation to solve for the mass:

59 N = m * 1.25 m/s²
m = 47.2 kg

So, if you raise the bag with an acceleration of 1.25 m/s², you can safely lift a maximum mass of 47.2 kg. Just be careful not to overload the bag, or you'll be in a real "tearable" situation!

To determine the greatest mass of groceries that can be lifted safely with the bag, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.

(a) If the bag is lifted with constant speed, it means there is no acceleration. In this case, the force acting on the bag will only be due to the weight of the groceries, which can be calculated using the formula F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

To find the greatest mass of groceries that can be lifted safely, we need to find the mass when the force exerted on the handles is equal to the maximum force the handles can withstand, which is 59 N.

59 N = m * 9.8 m/s^2

Rearranging the equation to solve for m:

m = 59 N / 9.8 m/s^2

m ≈ 6.02 kg

Therefore, the greatest mass of groceries that can be lifted safely with this bag, when it is raised with constant speed, is approximately 6.02 kg.

(b) If the bag is raised with an acceleration of 1.25 m/s^2, we need to consider the additional force due to the acceleration. The total force on the bag will be the sum of the force due to the weight of the groceries and the force due to the acceleration.

Since the maximum force the handles can withstand is still 59 N, we can set up the following equation:

59 N = (m * 9.8 m/s^2) + (m * 1.25 m/s^2)

Simplifying the equation:

59 N = m * (9.8 m/s^2 + 1.25 m/s^2)

59 N = m * (11.05 m/s^2)

Rearranging the equation to solve for m:

m = 59 N / 11.05 m/s^2

m ≈ 5.34 kg

Therefore, the greatest mass of groceries that can be lifted safely with this bag, when it is raised with an acceleration of 1.25 m/s^2, is approximately 5.34 kg.

To find the greatest mass of groceries that can be lifted safely with the bag, we need to consider the forces acting on the bag and the groceries.

(a) When the bag is raised with constant speed, it means that the net force acting on the bag is zero. Therefore, the weight of the groceries should be equal to the maximum force the handles can withstand.

Weight (W) = mass (m) × acceleration due to gravity (g)

Since the acceleration is zero, we can set up the equation:

W = m × g

The force applied to the handles should not exceed 59 N, which is equal to the weight of the groceries:

59 N = m × 9.8 m/s^2

Rearranging the equation, we can solve for the mass:

m = 59 N / 9.8 m/s^2

m ≈ 6.02 kg

Therefore, the greatest mass of groceries that can be lifted safely with the bag, when raised with constant speed, is approximately 6.02 kg.

(b) When the bag is raised with an acceleration of 1.25 m/s^2, we need to consider the additional force due to this acceleration. The force applied to the handles will be the sum of the weight of the groceries and the force due to acceleration.

Total force (F) = weight (W) + force due to acceleration

F = m × g + m × a

To find the maximum mass of groceries, we need to find the mass that corresponds to a total force of 59 N:

59 N = m × 9.8 m/s^2 + m × 1.25 m/s^2

Simplifying the equation:

59 N = (9.8 m/s^2 + 1.25 m/s^2) × m

59 N = 11.05 m/s^2 × m

Rearranging the equation, we can solve for the mass:

m = 59 N / 11.05 m/s^2

m ≈ 5.34 kg

Therefore, the greatest mass of groceries that can be lifted safely with the bag, when raised with an acceleration of 1.25 m/s^2, is approximately 5.34 kg.