Question

question 13
1 pts
a student sets a small box with a mass of \m\ on a platform scale. the object is tied to a piece of string which gently pulls upwards on the object with a force of $f_t$. the object remains motionless at rest on the scale and the scale still has a reading on it which is greater than zero. which of the following statements must be true about the scales measurement?

• the scale measures the normal force. the normal force in this case must be less than the weight.
• the scale measures the weight. in this case the weight is larger than the normal force.
• the scale measures the normal force. in this case the normal force must be exactly equal to the weight.

Explanation:

Step1: Analyze forces on the box

The box has three forces: weight \( W = mg \) (downward), tension \( F_T \) (upward), and normal force \( F_N \) (upward from the scale). Since it's at rest, \( \sum F = 0 \), so \( F_N + F_T = W \).

Step2: Determine what the scale measures

A platform scale measures the normal force (the force the box exerts on it, equal and opposite to \( F_N \) by Newton's third law).

Step3: Compare \( F_N \) and \( W \)

From \( F_N + F_T = W \), we can rearrange to \( F_N = W - F_T \). Since \( F_T>0 \) (the string pulls upward), \( F_N < W \).

Answer:

The scale measures the normal force. The normal force in this case must be less than the weight.