Bringing the Hammer Down – NOT!

Problem: Predict the mass of the hammer.

Support pole

Wstick

Whammer

The dashed segment in the FBD is not force. This should be obvious to you since it is not shown as a vector. There are only three forces, and as usual, each is labeled well.

My measurements from class (when I did my own in 2008):

  • The vertex of the angle is where the hammer touched the stick
  • The vertex of the angle is where the meter-stick reads “0”
  • The support pole makes contact where the stick reads “26.9” cm
  • The CM of the stick alone is about at the 50.3 cm mark
  • The CM of the hammer alone is 24 cm from the vertex
  • The mass of the stick alone was 95 grams.
  • The angle at the vertex was 10 degrees.

Error Correction: In period 4 on 1/10/08 (when I made up the problem), my initial plan of attack was bad. I put the origin at the vertex. (It was an initial guess.) Then I proceeded to balance the torques and my first attempt was difficult, because with the vertex as the origin, the support force from the pole exerts a torque with a lever arm equal to _____ cm. This is a hard way to attack the problem, given the unknown support force.

From Scott Wong’s suggestion, I put the origin at the pole itself. This made the analysis a fair bit simpler, because now the torque due to the pole is zero: not because the ______due to the pole was zero, but because the associated ______is now zero,and when lever arm is zero, leverage is zero, and by definition, torque = (leverage)x(force).

My solution requires the leverage of the torque due to the hammer’s weight. This leverage can be diagrammed above. (I put a dotted line in the diagram to help you.) Clearly construct and label this leverage in the diagram above, and then identify that length using the data. Then balance your CW and CCW torques and finish the problem.

The leverages referred to above all must be horizontal segments. This is because all forces are purely vertical. This becomes a very simple two-torque problem.

Answer:

The answer consistent with the above data is 682 grams.

When I put the hammer on the electronic scale, the scale said 696 grams.

Boo-ya-ka-sha!