Question

A body of mass 2kg falls from rest through a height of 20m and comes to rest having penetrated a distance of 0.5m into a sandy ground. Calculate the average force exerted by the sand in bringing the body to rest. (Take g=10ms^2

Answer 1

given m = 20 kg
u = 0
h = 20 m
we can find the value of v by using third equatuon of motion
v^2 = u^2 + 2 g h
v^2 = 0 + 2 *10 * 20
v^2 = 400
v= 20 m/s
this v will be initial velocity when the ball will hit the ground
we have to calculate the rate of retardation
by third equatuon
2 a s = V2 ^2 - V1 ^2
2 a 0.5 = 0 - 400
a = -400 m / s^2
now
F = ma
F = 20 * 400
F = 8000 Newton

Answer 2

Answer:

The common pressure exerted through the sand in bringing the object to relaxation is 800N.

Explanation:

From the above question,

They have given :

We can use the work-energy theorem to calculate the common pressure exerted via the sand in bringing the physique to rest.

The work-energy theorem states that the internet work executed on an object is equal to its exchange in kinetic energy.

               Net work executed = Change in kinetic energy

The work completed with the aid of gravity is equal to the gravitational possible electricity misplaced by way of the object as it falls via a top of 20m.

Work finished by means of gravity = mgh

Work finished by means of gravity = 2kg x 10m/$s^2$ x 20m

Work finished by means of gravity = 400J

The work performed by using the sand is equal to the pressure exerted with the aid of the sand increased with the aid of the distance penetrated via the object into the ground.

                  Work executed via sand = Fs x d

where Fs is the common pressure exerted via the sand, and d is the distance penetrated with the aid of the object into the ground. We want to remedy for Fs.

Since the object comes to rest, the internet work executed on the object is zero. Therefore:

Net work carried out = Work executed via gravity + Work completed by means of sand = 0

Substituting the values we have calculated, we get:

                      400J + Fs x 0.5m = 0

Solving for Fs, we get:

                      Fs = -800N

The bad signal shows that the pressure exerted by using the sand is in the contrary route to the displacement of the object. This is due to the fact the sand exerts a resistive pressure that opposes the action of the object.

Taking the magnitude of the force, we get:

                      |Fs| = 800N

Therefore, the common pressure exerted through the sand in bringing the object to relaxation is 800N.

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