Question

A jar of honey with a mass of 0.5 kgis nudged off the kitchen counter and falls 1 mto the floor. What force acts on the jar during its fall? How much work is done by this force?

Short answer

Step-by-step solution

Identification of the given data

The given data is listed below as,

• The mass of the honey jar is,$m=0.5kg$
• The distance at which the jar fall is,$d=1m$

Significance of the force exerted and the work done

The force exerted is the product of the mass of an object and the acceleration due to gravity (in the case of vertical movement of the object).

It is expressed as follows,

$F=mg$ ..(1)

Here, is the mass of the jar and is the acceleration due to gravity that is .

The work done is the product of the displacement of an object and the force exerted by the object.

Determination of the force on the jar

For$F=0.5kg$ and$g=9.8m/s^2$ in equation (1).

$$\begin{gathered} F=\left(0.5kg\right)\times \left(9.8m/s^2\right) \\ =4.9lgm/s^2\times \frac{1N}{1kgm/s^2} \\ =4.9N \end{gathered}$$

Since the force is acting in vertical downward direction so, $F=-4.9N$and its vector representation is,$\stackrel{\rightharpoonup }{F}=\left\{0,-49,0\right\}N$ .

Determination of the work done by the force

The equation of the work done on the jar is expressed as,

$W=Fd$

Here, F is the force acting and d is the distance of the jar.

For$F=4.9N$and $d=1m$,

$$\begin{gathered} W=\left(4.9N\right)\times \left(1m\right) \\ =4.9Nm \\ =4.9Nm\times \frac{1J}{1Nm} \\ =4.9J \end{gathered}$$

Thus, the force acting on the jar is and the work done by the force is $4.9J$.