Physics question

This forum made possible through the generous support of SDN members, donors, and sponsors. Thank you.
D

deleted647690

What is the tension in the string in trial 4 if the pendulum bob swings through equilibrium with a speed of 4 m/s? Mass of rope is 100 g, assume g = 10 m/s^2
A. 0.4 N
B. 0.6 N
C. 1.0 N
D. 1.4 N


I flipped through my class notes from physics, and could only find the equation, velocity = square root of T*L/m

Using this equation, I got A as an answer. However, the answer was D.

They used the equation: T - mg = mv^2/r

What is this? I never learned this equation in undergrad physics. I've noticed that BR physics questions often cover material that was never taught to me in my physics courses. Is this particular one necessary to know?

Members don't see this ad.
 
The net force (Fn) = mv^2/r is the centripetal force which also should equal the tension in the string (T) plus the weight of the string (-mg). Draw a free body diagram and it helps. If this was NOT a centripetal force problem then T-mg would equal ma. That's how I would solve it. Maybe someone else has a better reasoning.
 
The net force (Fn) = mv^2/r is the centripetal force which also should equal the tension in the string (T) plus the weight of the string (-mg). Draw a free body diagram and it helps. If this was NOT a centripetal force problem then T-mg would equal ma. That's how I would solve it. Maybe someone else has a better reasoning.


It didn't specifically mention centripetal force, but it was just a pendulum problem
 
It didn't specifically mention centripetal force, but it was just a pendulum problem

Most physics problems can be solved without resorting to memorized equations. Free-body diagrams are always the best first steps.

The pendulum is swinging, so you should immediately be reminded of centripetal force. What is centripetal force? Acceleration towards the center of the circle. What's providing that force? Well, there are only two forces acting on that pendulum - the tension in the string and the force of gravity. So which equation for centripetal force should you be using? Well, the fact that you're given velocity should immediately remind you of m*v^2/r.

So let's take the simplest case of the pendulum passing through a point that is perpendicular to the horizontal. At that point, there are two forces acting on the pendulum - tension and gravity. Let's denote that T and mg. These are in opposing directions, so let's define up as positive and down as negative. Thus, the net force is given by T - mg.

As I said above, the net force must be the force providing centripetal acceleration. Therefore, T - mg = m*v^2/r. Thus, T = m*g + m*v^2/r, which reduces to 0.1*10 + 0.1*16/r. You will need the radius of the rope to solve this problem.

You shouldn't rely on memorization of equations you were taught in physics class - you should instead rely on your critical analysis skills to come up with the relevant equations.
 
This is a critical thinking exam. It shouldn't have to mention centripetal force if you understand the concept.
 
Top