A2L Item 056

• Description: Compare the normal force on identical blocks in several different situations.
• Goal: Honing the concept of normal force and reasoning.
• Source: UMPERG-MOP
• Keywords: Forces, Mechanics

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The question for students:

Consider the five situations appearing below. All the blocks have the same size and density.

Which of the following statements is true regarding the normal force that the table or incline exerts on the block in contact with it?

1. N_D > N_C = N_A = N_E > N_B
2. N_D = N_A > N_C > N_E = N_B
3. N_C > N_D > N_A > N_E > N_B
4. N_D = N_A = N_C > N_E > N_B
5. N_A > N_D = N_C > N_B > N_E
6. N_D = N_A = N_E > N_C > N_B
7. More than one of the above is true.
8. None of the above is true.
9. Cannot be determined.

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Commentary for teachers:

Answer

(8) All that can be said with certainty is that none of the above is true. First, it is impossible to determine the relationship between N_B and N_E. Both are less than the weight, but which is least depends upon unknown angles and the tension in the rope. Further, N_C is largest because all of the other cases have a buoyancy force due to air. Some students may indicate (9) for the same reasons as stated above. However, technically, the truth or falsity of (1) to (7) can be determined.

Background

Students often think that the Normal force must be vertical because all of the examples they have seen are of this type. Other students may think that the deformed table is indicative of a greater (or lesser) normal force. A subtle issue is that the block under the bell jar will not have a buoyant force due to the air. While this is a small force, its absence means that the normal force in case C is largest of all.

Suggestions

Have students identify the basis of falseness of each of the statements.

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