Final answer:
The student's mass is calculated using the centripetal force formula Fc = m * v^2 / r. After substituting the given values and solving, the mass is found to be 75 kg. However, since this value is not listed in the options, the correct choice would be 'None of the above.'
Step-by-step explanation:
The question is asking to find a student's mass using the provided centripetal force, carousel radius, and the student's speed. We can use the formula for centripetal force, Fc = m * v2 / r, where Fc is the centripetal force, m is the mass, v is the velocity, and r is the radius of the circular path.
Substituting in the given values: 240 N = m * (4.0 m/s)2 / 5.0 m, we can solve for m (mass) as follows:
240 N = m * 16 m2/s2 / 5.0 m
240 N = m * 3.2 m/s2
m = 240 N / 3.2 m/s2
m = 75 kg
However, since this value is not listed in the multiple-choice options, we likely made a mistake in our calculations. Let's try again:
240 N = m * (4.0 m/s)2 / 5.0 m
240 N = m * (16 m2/s2) / 5.0 m
240 N = m * 3.2 m/s2
m = 240 N / 3.2 m/s2
m = 75 kg
After rechecking the calculations, the value of 75 kg remains constant. It appears that the multiple-choice options provided do not include the correct mass, which should be 75 kg based on the given information and the application of the centripetal force formula. Therefore, the correct response from the given options would be 'None of the above.'