Question

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question 33 of 62
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question 33
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a rope is tied to a 0.50 kg box and used to pull a box 2.5 m along a horizontal floor. the rope makes an angle of 42° with the horizontal and has a tension of 10 n. the opposing frictional force between the box and the floor is 1.8 n.
how much work is done by friction?
-4.5 j
4.5 j
3.3 j
-3.3 j

Explanation:

Step1: Recall Work Formula

Work \( W \) is given by \( W = F \cdot d \cdot \cos\theta \), where \( F \) is force, \( d \) is displacement, and \( \theta \) is the angle between force and displacement.

Step2: Identify Friction Force and Angle

Frictional force \( F_f = 1.8 \, \text{N} \), displacement \( d = 2.5 \, \text{m} \). Friction opposes motion, so \( \theta = 180^\circ \), and \( \cos(180^\circ) = -1 \).

Step3: Calculate Work Done by Friction

Substitute into the formula: \( W = 1.8 \times 2.5 \times \cos(180^\circ) \).
\( \cos(180^\circ) = -1 \), so \( W = 1.8 \times 2.5 \times (-1) = -4.5 \, \text{J} \).

Answer:

-4.5 J