F = MA Exam 2012 # 23 (Measuring local gravitational acceleration)

[SignaturePF]

Homework Statement

Which of the following sets of equipment cannot be used to measure the local value of the acceleration due to
gravity (g)?
(A) A spring scale (which reads in force units) and a known mass.
(B) A rod of known length, an unknown mass, and a stopwatch.
(C) An inclined plane of known inclination, several carts of different known masses, and a stopwatch.←
CORRECT
(D) A launcher which launches projectiles at a known speed, a projectile of known mass, and a meter stick.
(E) A motor with a known output power, a known mass, a piece of string of unknown length, and a stopwatch

The Attempt at a Solution

I eliminated A because that is a fundamental way to measure gravity, as a scale reads normal force. Simply place an object on flat ground where Normal force = mg, divide the known normal force by the known mass, and we have gravity.
I eliminated B since we can use uniform accelerated motion.
Δy = v_0t + 1/2at^2
since v_0 = 0
Δy = 1/2at^2, we also know t, so clearly we can find a
C I believed you could find, I'm not sure why you can't.
D I thought you could use projectile motion equations.
E I'm not sure.

 

[cepheid]

With C, having carts of several different masses is not that useful, because every mass will take the same time to get from the top of the incline to the bottom. The time depends only on the length of the incline, the inclination angle, and the acceleration due to gravity. So you really only need one cart, but you must also know the length of the incline. Perhaps you are meant to assume that you do NOT know this (because you have no metre stick)?

 

[cepheid]

For E, maybe you are supposed to try and wind the string (with mass hanging from it) onto the motor shaft at a constant speed, and since P = Fv, if you know v, you can find F, which is equal to mg (since the speed is constant, the lifting force must be balancing the weight). The thing I don't get is how you're supposed to get v with just a stopwatch and no known lengths. EDIT: Are you sure it wasn't a piece of string of *known* length?

 

[haruspex]

For E, you can use the motor and the stopwatch to deliver a known KE. Knowing the mass that tells you the speed. Use that to launch the mass vertically and time it to top of trajectory.

 

[Nickie]

The correct answer is C. A spring scale and known mass (A) can be used to measure gravity, as the normal force on the scale is equal to the weight of the object, which is directly proportional to gravity. A rod of known length, unknown mass, and stopwatch (B) can also be used to measure gravity, as the time it takes for the object to fall a certain distance can be used in the equation for uniform accelerated motion to calculate gravity. A launcher, known mass, and meter stick (D) can also be used to measure gravity, as the distance the projectile travels can be used in the equation for projectile motion to calculate gravity. However, an inclined plane, several carts of different known masses, and a stopwatch (C) cannot be used to measure gravity as the acceleration on an inclined plane is not the same as the local value of gravity. A motor with known output power, known mass, string of unknown length, and stopwatch (E) also cannot be used to measure gravity as the length of the string and the output power of the motor are not directly related to gravity.