To calculate the work done on the carton by the rope, we need to use the formula for work:
[tex]\[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \][/tex]
where:
- [tex]\( \text{Force} \)[/tex] is the force applied.
- [tex]\( \text{Distance} \)[/tex] is the distance over which the force is applied.
- [tex]\( \theta \)[/tex] is the angle between the direction of the force and the direction of the movement.
In this scenario:
- The force exerted by the rope, [tex]\( F \)[/tex], is [tex]\( 7 \, \text{N} \)[/tex].
- The distance the carton travels along the ramp, [tex]\( d \)[/tex], is [tex]\( 5.50 \, \text{m} \)[/tex].
- The direction of the force is parallel to the ramp’s surface, which means [tex]\( \theta = 0^\circ \)[/tex].
The cosine of [tex]\(0^\circ\)[/tex] is 1, i.e.,
[tex]\[ \cos(0^\circ) = 1 \][/tex]
So, the equation simplifies to:
[tex]\[ \text{Work} = 7 \, \text{N} \times 5.50 \, \text{m} \times 1 \][/tex]
Now, performing the multiplication:
[tex]\[ \text{Work} = 7 \, \times 5.50 \][/tex]
[tex]\[ \text{Work} = 38.5 \, \text{J} \][/tex]
Therefore, the work done on the carton by the rope is [tex]\( 38.5 \, \text{J} \)[/tex].
