A 200-kg crate is moved across a frictionless floor by applying a net force of 70 N for 5 seconds. This results in a final speed of 3 m/s after the crate moves a distance of 5m. What is the final kinetic energy of the crate?
KE=(mv^2)/2 = (200*3^2)/2 = 900J
The above is corect
The above is correct.
To find the final kinetic energy of the crate, we can use the formula for kinetic energy, which is given by:
Kinetic Energy = (1/2) * mass * velocity^2
In this case, we are given the mass of the crate (200 kg) and the final speed (3 m/s). We can calculate the final kinetic energy using these values.
The first step is to calculate the initial velocity of the crate. We know that the crate moves a distance of 5m in 5 seconds, so the average velocity can be calculated as:
Average velocity = distance / time = 5m / 5s = 1 m/s
Since the floor is frictionless, the net force applied is equal to the force required to accelerate the crate. Therefore, we can use Newton's second law of motion to find the acceleration of the crate.
Net force = mass * acceleration
70 N = 200 kg * acceleration
Solving for acceleration, we get:
acceleration = 70 N / 200 kg = 0.35 m/s^2
Now, we can use the equation of motion to find the final velocity. The equation is:
Final velocity = Initial velocity + (acceleration * time)
Initial velocity = Average velocity, as the crate starts from rest.
Final velocity = 1 m/s + (0.35 m/s^2 * 5 s)
Final velocity = 1 m/s + 1.75 m/s
Final velocity = 2.75 m/s
Now, we can substitute the values of mass (200 kg) and velocity (2.75 m/s) into the kinetic energy formula to find the final kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Kinetic Energy = (1/2) * 200 kg * (2.75 m/s)^2
Calculating this, we get:
Kinetic Energy ≈ 756.25 Joules
Therefore, the final kinetic energy of the crate is approximately 756.25 Joules.