Final answer:
The work done on the block by friction is calculated using the formula Work = Force × Distance × cos(θ), resulting in -225.0 Joules. The negative sign represents the work done against the motion of the block.
Step-by-step explanation:
To find the work done on the block by friction, we need to use the formula for work which is:
Work = Force × Distance × cos(θ)
Where the force is the friction force, the distance is the distance the block slides, and θ is the angle between the force and the direction of the motion. For kinetic friction, this angle is 180° because the friction force acts in the opposite direction to the block's motion.
Let's plug in the values:
- Force of friction (Φ) = 30.0 N
- Distance (d) = 7.50 m
- θ = 180° because friction acts opposite to motion
Work done by friction (W) = 30.0 N × 7.50 m × cos(180°)
Cosine of 180° is -1, so:
W = 30.0 N × 7.50 m × -1
W = -225.0 J
The negative sign indicates the work done by the friction force acts to reduce the kinetic energy of the block.