a body of weight 30 N falls freely from a height of 15m and burrows into sand through a distance of 0.5 m. find the resistance due to sand
To find the resistance due to sand, we can use the concept of work-energy. The work done on the body by the sand is equal to the change in its kinetic energy.
First, let's calculate the initial potential energy of the body at a height of 15 m. The potential energy (PE) is given by the equation:
PE = m * g * h
where:
m = mass of the body
g = acceleration due to gravity (approximated as 9.8 m/s^2 for Earth)
h = height
Since we know the weight of the body (which is equal to the force of gravity acting on it), we can use the equation:
Weight = m * g
Rearranging the equation to solve for mass:
m = Weight / g
Now we can substitute the values:
Weight = 30 N
g = 9.8 m/s^2
m = 30 N / 9.8 m/s^2 = 3.06 kg (approx)
Next, let's calculate the change in kinetic energy. The kinetic energy (KE) is given by the equation:
KE = (1/2) * m * v^2
where:
m = mass of the body
v = final velocity of the body
Since the body started from rest, the initial velocity (u) is 0 m/s. So, the change in kinetic energy is:
ΔKE = KE - KE_initial
= KE - 0
= KE
Now, we need to find the final velocity (v). We can use the equation of motion:
v^2 = u^2 + 2 * a * s
where:
u = initial velocity
a = acceleration
s = distance covered
In this case, the body falls freely under the influence of gravity, so the acceleration (a) is equal to the acceleration due to gravity (g), and the initial velocity (u) is 0 m/s.
v^2 = 0^2 + 2 * 9.8 m/s^2 * 0.5 m
v^2 = 0 + 9.8 m/s^2 * 0.5 m
v^2 = 4.9 m^2/s^2
v ≈ 2.21 m/s (approx)
Now, let's calculate the change in kinetic energy.
ΔKE = KE
= (1/2) * m * v^2
= (1/2) * 3.06 kg * (2.21 m/s)^2
≈ 6.43 J (approx)
As mentioned earlier, the work done on the body by the sand is equal to the change in its kinetic energy. Therefore, the resistance due to sand is approximately 6.43 Joules.