**AP Physics 1 Question 290: Answer and Explanation**

### Test Information

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**Question: 290**

**8.** As a pendulum swings back and forth, it is affected by two forces: gravity and tension in the string. Splitting gravity into component vectors, as shown above, produces *mg* sin*θ* (the restoring force) and *mg* cos*θ*. Which of the following correctly describes the relationship between the magnitudes of tension in the string and *mg* cos*θ*?

- A. Tension >
*mg*cos*θ* - B. Tension =
*mg*cos*θ* - C. Tension <
*mg*cos*θ* - D. The relationship depends on the position of the ball.

**Correct Answer:** D

**Explanation:**

**D**

Whenever the ball is in motion, it will be experiencing circular motion, which means there must be a centripetal force. Centripetal force is a net force toward the center, so that means tension must be the greater force whenever the ball is moving. However, the ball is not always moving. At the two extreme edges of its motion, the ball is motionless for an instant as it changes directions. At those times, the net centripetal force is zero, meaning the two given forces are equal.