Hi! I have some questions from a study guide in my physics class, and they give me the answer, but I have to show how to get the answer. I did most of them, but need help with these. Here is problem #6:
A 30 kg kid on rollerskates is moving 1 m/s. His brother pushes him with a force of 5 N. What will be his kinetic energy after his brother pushes him 4.0 m? (35 J)
To calculate the kinetic energy of the kid after his brother pushes him, you need to use the formula for kinetic energy:
Kinetic energy (KE) = 0.5 * mass * velocity².
In this case, the mass of the kid is given as 30 kg, and his initial velocity is given as 1 m/s. However, his velocity will change after he is pushed, so we need to calculate the final velocity before we can find the kinetic energy.
To find the final velocity, we can use Newton's second law of motion, which states that the force applied to an object is equal to the product of its mass and acceleration:
Force (F) = mass (m) * acceleration (a).
In this case, the applied force is 5 N, and the mass of the kid is 30 kg. We don't know the acceleration of the kid, so let's rearrange the formula to solve for acceleration:
Acceleration = Force / mass.
Using the given values:
Acceleration = 5 N / 30 kg = 0.1667 m/s².
Now that we have the acceleration, we can use the equation of motion to find the final velocity. The equation is:
Final velocity² = Initial velocity² + 2 * acceleration * displacement.
In this case, the initial velocity is 1 m/s, the acceleration is 0.1667 m/s², and the displacement is 4.0 m. Let's plug those values into the equation:
Final velocity² = 1² + 2 * 0.1667 m/s² * 4.0 m
= 1 + 1.3336 m²/s²
= 2.3336 m²/s².
Taking the square root of both sides, we find that the final velocity is approximately 1.528 m/s.
Now that we have the final velocity, we can calculate the kinetic energy using the formula:
KE = 0.5 * mass * velocity².
Plugging in the values, we get:
KE = 0.5 * 30 kg * (1.528 m/s)²
≈ 0.5 * 30 kg * 2.3336 m²/s²
≈ 35 J.
Therefore, the kinetic energy of the kid after his brother pushes him 4.0 m will be approximately 35 J.