Question

read each scenario and then answer the questions.
scenario a: a shopping cart is pushed a distance of 3 m by a force of 15 n.
scenario b: a shopping cart is pushed a distance of 4 m by a force of 12 n.
scenario c: a shopping cart is pushed a distance of 6 m by a force of 10 n.
which scenario requires the most work?
which scenario requires the least work?

Explanation:

Step1: Recall the work formula

The formula for work is \( W = F \times d \), where \( W \) is work, \( F \) is force, and \( d \) is distance.

Step2: Calculate work for Scenario A

For Scenario A: \( F = 15\ N \), \( d = 3\ m \). So \( W_A = 15 \times 3 = 45\ J \).

Step3: Calculate work for Scenario B

For Scenario B: \( F = 12\ N \), \( d = 4\ m \). So \( W_B = 12 \times 4 = 48\ J \).

Step4: Calculate work for Scenario C

For Scenario C: \( F = 10\ N \), \( d = 6\ m \). So \( W_C = 10 \times 6 = 60\ J \).

Step5: Compare the work values

We have \( W_A = 45\ J \), \( W_B = 48\ J \), \( W_C = 60\ J \). So \( W_C > W_B > W_A \).

Answer:

Most work: Scenario C; Least work: Scenario A