A 0.5 kg air-hockey puck is initially at rest. What will its kinetic energy be after a net force of 0.8 N acts on it for a distance of 0.5 m?
KE=W =Fs =0.8•0.5 = 0.4 J
Well, if the air-hockey puck has a net force of 0.8 N acting on it for a distance of 0.5 m, I think it's safe to say it's going to have quite the workout! Now, to calculate its kinetic energy, we need to use the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Since the puck starts from rest and we're given the force applied (0.8 N), we can find its acceleration using Newton's second law:
force = mass * acceleration
Rearranging the formula, we have:
acceleration = force / mass
acceleration = 0.8 N / 0.5 kg
acceleration = 1.6 m/s^2
Now, let's find the final velocity using one of Newton's motion equations:
vf^2 = vi^2 + 2 * acceleration * distance
Since the initial velocity (vi) is 0 m/s, we can simplify the equation to:
vf^2 = 2 * acceleration * distance
vf^2 = 2 * 1.6 m/s^2 * 0.5 m
vf^2 = 1.6 m^2/s^2
vf = √(1.6 m^2/s^2)
vf ≈ 1.26 m/s
Finally, let's substitute the values into the kinetic energy formula:
Kinetic Energy = (1/2) * mass * velocity^2
Kinetic Energy = (1/2) * 0.5 kg * (1.26 m/s)^2
Kinetic Energy ≈ 0.3975 Joules
So, after that net force of 0.8 N acts on the 0.5 kg air-hockey puck for a distance of 0.5 m, its kinetic energy will be approximately 0.3975 Joules. It's ready to slide and glide like a champion!
To find the kinetic energy of an object, we can use the equation:
Kinetic Energy = (1/2) * mass * velocity^2
Given that the mass of the air-hockey puck is 0.5 kg and it is initially at rest, the initial velocity (v₀) is 0 m/s.
Now we need to find the final velocity (v). We can use the equation of motion:
force = mass * acceleration
Considering the net force acting on the puck:
0.8 N = 0.5 kg * acceleration
Rearranging the equation, we find:
acceleration = 0.8 N / 0.5 kg = 1.6 m/s²
The net force acting on the puck is given by Newton's second law of motion:
force = mass * acceleration
0.8 N = 0.5 kg * 1.6 m/s²
Now, we can use the equation of motion:
v² = v₀² + 2 * acceleration * distance
Given that the initial velocity (v₀) is 0 m/s, and the distance (d) is 0.5 m, we can substitute the values into the equation:
v² = 0 + 2 * 1.6 m/s² * 0.5 m
v² = 1.6 m²/s²
Taking the square root of both sides, we can find the final velocity (v):
v = √1.6 m²/s²
v ≈ 1.26 m/s
Now, we can calculate the kinetic energy using the equation mentioned earlier:
Kinetic Energy = (1/2) * mass * velocity^2
Kinetic Energy = (1/2) * 0.5 kg * (1.26 m/s)^2
Kinetic Energy ≈ 0.396 J
Therefore, the kinetic energy of the air-hockey puck after a net force of 0.8 N acts on it for a distance of 0.5 m will be approximately 0.396 Joules.
To find the kinetic energy of the air-hockey puck after the net force has acted on it for a certain distance, we need to use the work-energy theorem.
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be expressed as:
Work = Change in kinetic energy
In this case, the net force (F) acts on the puck for a distance (d), so the work done on the puck is given by:
Work = Force * Distance
Therefore, the work done on the puck is: 0.8 N * 0.5 m = 0.4 J (joules).
Since the work done on the puck is equal to the change in its kinetic energy, we can write:
Change in kinetic energy = 0.4 J
However, the puck starts from rest, so its initial kinetic energy is zero. Therefore, the final kinetic energy of the puck will be 0.4 J.
In conclusion, the kinetic energy of the air-hockey puck after a net force of 0.8 N acts on it for a distance of 0.5 m will be 0.4 joules.