# A floating ice block is pushed through a displacement d=(15m)i-(12m)j along a straight embankment by rushing water, which exerts a force F=(210N)i-(150N)j on the block. How much work does theforce do on the block during the displacement?

A floating ice block is pushed through a displacement d=(15m)i-(12m)j along a straight embankment by rushing water, which exerts a force F=(210N)i-(150N)j on the block. How much work does theforce do on the block during the displacement?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Jozlyn
The work done W = F.d
$=\left(210i-150j\right)\cdot \left(15i-12j\right)$
$=3150i-1800j$
Thus, magnitude of the work done $W={\left({F}_{x}^{2}+{F}_{y}^{2}\right)}^{\frac{1}{2}}$
Or $W=3.63\cdot {10}^{3}$ J
###### Not exactly what you’re looking for?
Jeffrey Jordon

Solution

We find the work done by the water on the ice block:

$W=\stackrel{\to }{F}\cdot \stackrel{\to }{d}$

$=\left[\left(210N\right)\stackrel{^}{i}-\left(150N\right)\stackrel{^}{j}\right]\cdot \left[\left(15m\right)\stackrel{^}{i}-\left(12m\right)\stackrel{^}{j}\right]$

=(210 N)(15 m)+(-150 N)(-12 m)