A 0.5 kg air-hockey puck is initially at rest. What will its kinetic energy be after a net force of 0.3 N acts on it for a distance of 0.5 m
work done = .3*.5 .15 Joules
so
(1/2) m v^2 = .15
To find the kinetic energy (KE) of the air-hockey puck, we need to use the formula:
KE = 0.5 * m * v^2
where m is the mass of the puck and v is its final velocity.
Given:
mass (m) = 0.5 kg
net force (F) = 0.3 N
distance (d) = 0.5 m
First, we can use Newton's second law of motion to find the acceleration (a) of the puck:
F = m * a
0.3 N = 0.5 kg * a
a = 0.3 N / 0.5 kg
a = 0.6 m/s^2
Next, we can use the equation of motion to find the final velocity (v) of the puck:
v^2 = u^2 + 2 * a * d
Since the puck starts from rest (u = 0 m/s), the equation simplifies to:
v^2 = 2 * a * d
v^2 = 2 * 0.6 m/s^2 * 0.5 m
v^2 = 0.6 m^2/s^2
Taking the square root of both sides:
v = √(0.6 m^2/s^2)
v ≈ 0.7746 m/s
Finally, we can calculate the kinetic energy (KE) using the formula:
KE = 0.5 * m * v^2
KE = 0.5 * 0.5 kg * (0.7746 m/s)^2
KE ≈ 0.0946 Joules
Therefore, the kinetic energy of the air-hockey puck will be approximately 0.0946 Joules after the net force of 0.3 N acts on it for a distance of 0.5 m.
To find the kinetic energy of the air-hockey puck, we need to use the following formula:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
Given that the mass of the air-hockey puck is 0.5 kg and it is initially at rest, we need to find the velocity (v) first.
To find the velocity, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. Here, the net force acting on the puck is 0.3 N, and we can find the acceleration (a) using the formula:
Force (F) = mass (m) * acceleration (a)
Given that the force (F) is 0.3 N and the mass (m) is 0.5 kg, we can rearrange the equation to solve for acceleration:
a = F / m
a = 0.3 N / 0.5 kg
a = 0.6 m/s^2
Now that we have the acceleration, we can find the velocity using the kinematic equation:
v^2 = u^2 + 2 * a * s
In this case, the initial velocity (u) is zero because the puck is initially at rest, the acceleration (a) is 0.6 m/s^2, and the distance (s) is 0.5 m.
v^2 = 0^2 + 2 * 0.6 m/s^2 * 0.5 m
v^2 = 0 + 0.6 m^2/s^2
v^2 = 0.3 m^2/s^2
Taking the square root of both sides, we find:
v = √(0.3 m^2/s^2)
v ≈ 0.5477 m/s
Now that we have the velocity (v), we can substitute it into the formula for kinetic energy (KE) to find the answer:
KE = 1/2 * mass * velocity^2
KE = 1/2 * 0.5 kg * (0.5477 m/s)^2
KE ≈ 0.075 joules
Therefore, the kinetic energy of the air-hockey puck after a net force of 0.3 N acts on it for a distance of 0.5 m is approximately 0.075 joules.