A child pushes, with F_{1}, his sister on a swing, generating torque, τ_{1} which causes her to swing forward. If he then gets in a swing that hangs on a chain that is 20% shorter and his sister pushes with a force, F_{2}, that is directed at a 30º angle to the swing, what is the relationship between F_{1} and F_{2} if they generate the same torque?
A) F_{1} = F_{2}
B) 2.5 F_{1} = F_{2}
C) F_{1} = 2.5 F_{2}
D) 2 F_{1} = F_{2}
Explanation
The equation for torque is given by:
τ = rF sin θ
where r is the distance between the fulcrum and the force, F is the applied force, and θ is the angle between the applied force and the lever arm.
For the boy, we can write the following equation:
τ_{1} = r_{1}F_{1}
The original question does not specify an angle for the boy. On the MCAT, if you’re not told otherwise then assume that θ is 90º in a torque problem and thus that sin θ is 1.
For the sister, we can write the following equation:
τ_{2} = r_{2}F_{2} sin θ_{2}
We are told that the length of the swing is 20% shorter and that she pushes with a force that is directed at 30º. Thus we may say that r_{2} = 0.8r_{1} and the equation becomes:
τ_{2} = 0.8r_{1}F_{2} sin 30
τ_{2} = 0.8r_{1}F_{2} (0.5)
τ_{2} = 0.4r_{1}F_{2}
Finally, we’re told that both torques are the same, so we may set them equal:
τ_{2} = 0.4r_{1}F_{2 }= τ_{1} = r_{1}F_{1}
0.4r_{1}F_{2 }= r_{1}F_{1}
0.4F_{2 }= F_{1}
So, the answer is:
B) 2.5 F_{1} = F_{2}
Want more MCAT practice?
We’ve got options for every schedule and learning style!
From the best online MCAT course created by top instructors with 524+ MCAT scores to the most representative fulllength practice exams and private tutoring, we can custom tailor your MCAT prep to your goals!
Not sure which option is right for you? Schedule a free MCAT consultation with an MCAT Advisor using the form below. No obligation, just expert advice.
Search the Blog
Free Consultation
Interested in our Online MCAT Course, OneonOne MCAT Tutoring or Med admissions packages? Set up a free consultation with one of our experienced Senior Student Advisors.
Schedule NowPopular Posts

MCAT Blog What's on the MCAT?

MCAT Blog How to Review MCAT Full Lengths
Free MCAT Practice Account
Need great MCAT practice?Get the most representative MCAT practice possible when you sign up for our free MCAT Account, which includes a halflength diagnostic exam and one of our fulllength MCAT practice exams.
Learn More