A gardener uses a wheelbarrow to move soil from a truck to his garden. On the first trip from the truck to the garden, the wheelbarrow is half-full of soil and the gardener applies a certain force to cause it to accelerate. On the second trip, the wheelbarrow is full of soil. Although the gardener applies the same amount of force to the wheelbarrow, he cannot move it with the same rate of acceleration. What should the gardener do to move the wheelbarrow at the same rate of acceleration for the second trip?

Question

A gardener uses a wheelbarrow to move soil from a truck to his garden. On the first trip from the truck to the garden, the wheelbarrow is half-full of soil and the gardener applies a certain force to cause it to accelerate. On the second trip, the wheelbarrow is full of soil. Although the gardener applies the same amount of force to the wheelbarrow, he cannot move it with the same rate of acceleration. What should the gardener do to move the wheelbarrow at the same rate of acceleration for the second trip?
 A. 
keep the amount of soil the same and apply less force
 B. 
reduce the amount of soil by one-half and apply the same amount of force
 C. 
double the amount of soil, and apply less force
 D. 
reduce the amount of soil by one-quarter and apply the same amount of force

GPT-4o mini · Answer

To analyze the situation, we can refer to Newton's second law, which states that Force (F) equals mass (m) times acceleration (a) or F = ma.

On the first trip, the wheelbarrow is half-full, and the gardener applies a certain force to achieve a certain acceleration. On the second trip, when the wheelbarrow is full of soil, its mass has increased. If the gardener applies the same force but the mass (and therefore the weight) of the wheelbarrow plus soil is greater, the acceleration will be less instead of remaining the same.

To keep the acceleration constant (the same as the first trip), the gardener needs to reduce the overall mass being moved while maintaining the same force.

Now let’s examine the options:

A. Keep the amount of soil the same and apply less force.

This will not achieve the same acceleration since reducing the force while keeping the mass constant would reduce the acceleration.

B. Reduce the amount of soil by one-half and apply the same amount of force.

This decreases the mass in the wheelbarrow to the same level as in the first trip, allowing the force to produce the same acceleration.

C. Double the amount of soil and apply less force.

This contradicts the needed condition; more mass would require more force to maintain the same acceleration.

D. Reduce the amount of soil by one-quarter and apply the same amount of force.

This still keeps the mass above what it was in the first trip, leading to a smaller acceleration than initially desired.

Thus, the correct answer is B: reduce the amount of soil by one-half and apply the same amount of force. This option ensures that the mass is the same as in the first trip, allowing the gardener to achieve the same rate of acceleration.