Floating Ice Block A floating ice block is pushed through a displacement
along a straight embankment by rushing water, which exerts a force
on the block. How much work does the force do on the block during the displacement
The Correct Answer and Explanation is:
To determine how much work the force does on the ice block during the displacement, we use the physics definition of work:Work=F⃗⋅d⃗=Fdcos(θ)\text{Work} = \vec{F} \cdot \vec{d} = Fd\cos(\theta)Work=F⋅d=Fdcos(θ)
Where:
- FFF is the magnitude of the force applied by the rushing water
- ddd is the magnitude of the displacement
- θ\thetaθ is the angle between the direction of the force and the direction of the displacement
- F⃗⋅d⃗\vec{F} \cdot \vec{d}F⋅d denotes the dot product of the force and displacement vectors
Correct Answer:
The exact value of the work depends on the given numerical values for force, displacement, and the angle between them. If the force is in the same direction as the displacement (which is likely for water pushing a floating ice block along a straight path), then:θ=0∘⇒cos(0∘)=1\theta = 0^\circ \quad \Rightarrow \quad \cos(0^\circ) = 1θ=0∘⇒cos(0∘)=1
So the work simplifies to:Work=Fd\text{Work} = FdWork=Fd
Thus, the force does an amount of work equal to the product of its magnitude and the displacement of the ice block, assuming the force is applied in the direction of motion.
Explanation:
Work in physics refers to the process of energy transfer when a force causes an object to move. When rushing water pushes an ice block along a straight embankment, the water exerts a continuous force in the direction of the movement. If the force and displacement are aligned, then all of the applied force contributes to moving the ice block, resulting in maximum work done.
Mathematically, work is calculated using the dot product of the force vector and the displacement vector. The formula W=Fdcos(θ)W = Fd\cos(\theta)W=Fdcos(θ) reflects this, where θ\thetaθ is the angle between the direction of the applied force and the direction of motion. When θ\thetaθ is zero degrees, the cosine of zero is one, meaning the full force contributes to the work. If the angle were different, only the component of the force in the direction of the displacement would be doing the work.
In the context of the floating ice block, since it moves along a straight path and the water pushes it forward, the angle between force and displacement is likely zero. This means the full magnitude of the force is responsible for moving the ice, and the work done is simply the product of the force and the displacement.
Understanding this helps explain how energy from moving water can transfer to objects like floating ice and cause them to move downstream.
