A body of mass 0.05kg falls from the height of 3m into a pile of send .the body penetrates the sand to a distant of 0.03m before stopping .what force is exerted by the sand
Data:- m=0.05kg
U=0 m/s
G=9.8m/s
S=3m
Formula:- """ V²=u²+2gs""""
V²=(0)²+2(9.8)×3
V²=0+19.6×3
V²=58.8
V=√58.8
="""""V=7.66m/s""""
Data:-
V=7.66m/s
S=0.03m
V=0
a=?
Formula:-. """" V²=u²+2as""""
i.e. a=v²-u²/2s
a=(7.66)²-(0)²/2(0.03)
a=58.67-0/0.06
a=58.67/0.06
""""a=977.83m/s²""
Force=?
We know that,
F= ma
F=0.05×977.83
""""""F=48.8915N"""""
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-7.5n
force*distance=.05*9.8*3
solve for force
To determine the force exerted by the sand on the body, we can use the concept of work done. The work done on an object is equal to the force applied multiplied by the distance over which the force is applied.
In this case, the force exerted by the sand can be found by calculating the work done on the body as it penetrates the sand. The work done can be calculated using the formula:
Work = Force × Distance
The work done on the body is equal to its change in potential energy as it falls into the sand. The potential energy of an object is given by the formula:
Potential energy = mass × gravitational acceleration × height
In this case, the height is the distance the body falls, which is 3m. The mass is 0.05kg, and the gravitational acceleration is approximately 9.8 m/s².
Potential energy = 0.05kg × 9.8 m/s² × 3m
Now, since the body penetrates the sand to a depth of 0.03m (distance), we can assume that the sand exerts an equal and opposite force to stop the body. Therefore, the work done by the sand is equal to the negative of the potential energy (since work done is negative when force is opposite to the displacement):
Work = -Potential energy
Substituting the values, we have:
Work = -(0.05kg × 9.8 m/s² × 3m)
Finally, to find the force exerted by the sand, we divide the work by the distance over which the force is applied, which is the penetration distance:
Force = Work / Distance
Substituting the values, we have:
Force = -(0.05kg × 9.8 m/s² × 3m) / (0.03m)