Question

How much work is done against gravity in lifting a $6.00-\mathrm{kg}$ weight through a distance of $20.0\mathrm{cm}?$

Short answer

Answer: The work done against gravity is 11.772 J.

Step-by-step solution

Convert distance

First, we need to convert the given distance from centimeters to meters, since we'll be working in SI units. To do this, remember that there are $100$ centimeters in a meter: $20.0\mathrm{cm}=20.0/100\mathrm{m}=0.200\mathrm{m}$.

Calculate gravitational force

Next, we need to find the gravitational force acting on the weight. This is given by the formula $F=m\times g$, where $m$ is the mass of the weight and $g$ is the gravitational acceleration ($9.81\mathrm{m}/{\mathrm{s}}^2$). So the gravitational force is: $F=6.00\mathrm{kg}\times 9.81\mathrm{m}/{\mathrm{s}}^2=58.86\mathrm{N}$.

Compute work done against gravity

Now that we have the distance and the gravitational force, we can calculate the work done against gravity using the formula for work: $W=F\times d\times \cos \theta$. Since the angle is $0^{\circ }$, the cosine of the angle is $1$. Therefore, the work done against gravity is: $W=58.86\mathrm{N}\times 0.200\mathrm{m}\times 1=11.772\mathrm{J}$ (joules). So, the work done against gravity in lifting the $6.00-\mathrm{kg}$ weight through a distance of $20.0\mathrm{cm}$ is $11.772\mathrm{J}$.