a body of mass 10kg and initially at rest is subjected to a force of 20N through a distance of 10m calculates the change in kinetic energy of the body
The change in kinetic energy of an object can be calculated using the equation:
ΔKE = 1/2 * m * (v^2 - u^2)
where:
ΔKE = change in kinetic energy
m = mass of the object (in kg)
u = initial velocity of the object (in m/s)
v = final velocity of the object (in m/s)
In this case, the mass of the object is given as 10 kg and it is initially at rest (u = 0 m/s). Therefore, u^2 = 0.
To find the final velocity (v), we need to use Newton's second law of motion:
F = ma
where:
F = force applied on the object (in N)
m = mass of the object (in kg)
a = acceleration of the object (in m/s^2)
Rearranging the equation to solve for acceleration:
a = F / m
Substituting the given values:
a = 20 N / 10 kg
a = 2 m/s^2
Now, we can use the equation to calculate the final velocity (v):
v^2 = u^2 + 2a * s
where:
s = distance traveled by the object (in m)
Substituting the given values:
v^2 = 0 + 2 * 2 m/s^2 * 10 m
v^2 = 40 m^2/s^2
Taking the square root of both sides to find v:
v = √40 m/s
v ≈ 6.32 m/s
Now that we have the final velocity, we can calculate the change in kinetic energy:
ΔKE = 1/2 * m * (v^2 - u^2)
ΔKE = 1/2 * 10 kg * (6.32^2 - 0^2)
ΔKE ≈ 1/2 * 10 kg * (39.94 m^2/s^2)
ΔKE ≈ 199.7 J
Therefore, the change in kinetic energy of the body is approximately 199.7 Joules.
To calculate the change in kinetic energy of the body, we need to use the work-energy theorem. The work done on an object is equal to the change in its kinetic energy.
The work done (W) can be calculated using the formula:
W = Force * Distance
Given that the force, F = 20 N, and the distance, d = 10 m, we can substitute these values into the formula:
W = 20 N * 10 m
W = 200 Nm
Since work is equal to the change in kinetic energy (ΔKE), we have:
ΔKE = 200 Nm
Thus, the change in kinetic energy of the body is 200 Nm.