A net force of 44N accelerates a 5.4-kg mass over a distance of 13 m.
a. What is the increase in kinetic energy of the mass?
work in = 44* 13 = 572 Joules
which is the increase in kinetic energy
To find the increase in kinetic energy of the mass, we need to know the formula for calculating kinetic energy. The formula for kinetic energy is:
Kinetic energy (KE) = 1/2 * mass * velocity^2
However, we are given the force and distance, so we first need to calculate the velocity. To do that, we can use Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
Rearranging the equation, we get:
acceleration (a) = Force (F) / mass (m)
Given that the force is 44N and the mass is 5.4kg, we can plug in these values to find the acceleration:
a = 44N / 5.4kg
a ≈ 8.15 m/s^2
Now that we have the acceleration, we can calculate the final velocity using the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity (usually assumed to be zero when an object starts from rest)
a = acceleration
s = distance
Since the initial velocity is assumed to be zero, we can simplify the equation to:
v^2 = 2as
Plugging in the values, we get:
v^2 = 2 * 8.15 m/s^2 * 13 m
v ≈ sqrt(212.9 m^2/s^2)
v ≈ 14.59 m/s
Now that we have the final velocity, we can calculate the increase in kinetic energy:
KE = 1/2 * m * (v^2 - u^2)
Since u is assumed to be zero, we can simplify the equation to:
KE = 1/2 * m * v^2
Plugging in the values, we get:
KE = 1/2 * 5.4 kg * (14.59 m/s)^2
KE ≈ 1/2 * 5.4 kg * 212.9 m^2/s^2
KE ≈ 576.486 J
Therefore, the increase in kinetic energy of the mass is approximately 576.486 Joules.