Final answer:
The kinetic energy of the rolling suitcase after being pulled for 7 m is approximately 98√3 J.
Step-by-step explanation:
The kinetic energy of an object can be calculated using the equation KE = 1/2 * mv^2, where KE represents the kinetic energy, m is the mass of the object, and v is the velocity of the object.
In this case, the rolling suitcase has a mass of 23 kg. To find its velocity after being pulled for 7 m, we need to calculate the acceleration first.
Since the pulling force is at an angle of 30°, we can find the horizontal component of the force by multiplying the force by the cosine of the angle.
The horizontal component of the force is equal to 4 N * cos(30°) = 4 N * √3/2 = 4√3/2 N. Since the horizontal force is responsible for the acceleration, we can use Newton's second law, F = ma, to find the acceleration.
The acceleration is equal to the horizontal force divided by the mass of the suitcase, which is (4√3/2 N) / 23 kg = (2√3/23) m/s².
Now we can use the kinematic equation, v² = u² + 2as, to find the final velocity of the suitcase.
Since the initial velocity is 0 m/s, the equation becomes v² = 2 * (2√3/23) m/s² * 7 m = 14√3/23 m/s.
Finally, we can calculate the kinetic energy using the formula KE = 1/2 * mv^2. Substituting the mass and the velocity, we get KE = 1/2 * 23 kg * (14√3/23 m/s)^2 = 98√3 J.