# How much work does it take to lift a 35 kg  weight 1/2 m ?

Mar 17, 2018

171.5 J

#### Explanation:

The amount of work required to complete an action can be represented by the expression $F \cdot d$, where F represents the force used and d represents the distance over which that force is exerted.

The amount of force required to lift an object is equal to the amount of force required to counteract gravity. Assuming the acceleration due to gravity is $- 9.8 \frac{m}{s} ^ 2$, we can use Newton’s second law to solve for the force of gravity on the object.

${F}_{g} = - 9.8 \frac{m}{s} ^ 2 \cdot 35 k g = - 343 N$

Because gravity applies a force of -343N, to lift the box one must apply a force of +343N. In order to find the energy required to lift the box half a meter, we must multiply this force by half a meter.

$343 N \cdot 0.5 m = 171.5 J$

Mar 18, 2018

$171.5 \setminus \text{J}$

#### Explanation:

We use the work equation, which states that

$W = F \cdot d$

where $F$ is the force applied in newtons, $d$ is the distance in meters.

The force here is the weight of the box.

Weight is given by

$W = m g$

where $m$ is the mass of the object in kilograms, and $g$ is the gravitational acceleration, which is approximately $9.8 \setminus {\text{m/s}}^{2}$.

So here, the weight of the box is

$35 \setminus \text{kg"*9.8 \ "m/s"^2=343 \ "N}$.

The distance here is $\frac{1}{2} \setminus \text{m"=0.5 \ "m}$.

So, plugging in the given values into the equation, we find that

$W = 343 \setminus \text{N"*0.5 \ "m}$

$= 171.5 \setminus \text{J}$

Note that I used $g = 9.8 \setminus {\text{m/s}}^{2}$ to calculate the weight of the box.