Answered

A roller coaster at an amusement park starts from rest, and accelerates to reach a velocity which is 2.5 m/s.

The roller coaster is subjected to a parallel force of 300N for a distance of 15 m.

What is the mass of the roller coaster?



Answer :

MathPhys

Answer:

1440 kg

Explanation:

There are two ways to solve this problem. One method is the work-energy theorem, which says the work done on an object is equal to the change in kinetic energy. The other method is to use kinematics to calculate the acceleration, then use Newton's second law of motion to find the mass.

Using work-energy theorem:

W = Ī”KE

Fd = Ā½ mvĀ²

m = 2Fd / vĀ²

m = 2 (300 N) (15 m) / (2.5 m/s)Ā²

m = 1440 kg

Alternatively, using kinematics to find the acceleration:

vĀ² = uĀ² + 2as

(2.5 m/s)Ā² = (0 m/s)Ā² + 2a (15 m)

a = 0.208 m/sĀ²

From Newton's second law:

F = ma

m = F / a

m = (300 N) / (0.208 m/sĀ²)

m = 1440 kg

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