The Atwood Machine Formal Lab Report Atwoods Machine

The Atwood Machine Formal Lab Report

Atwood’s Machine n The purpose of this laboratory exercise is to investigate the validity of Newton’s Second Law of Motion. You will use a single pulley apparatus as shown. This apparatus is commonly referred to as an “Atwood Machine”. The Atwood Machine allows one object to hoist another object using only gravity.

Atwood’s Machine n To determine the tension in the string (FT), we have to draw a free-body diagram FT FT M 1 Fgm 1 M 2 Fgm 2

Making Sense Of It! n n n Fm 2 = m 2 a = m 2 g – FT and Fm 1 = m 1 a = -m 1 g + FT How can we simplify this? Eqn 1 Eqn 2

Here’s How! n n n We can determine the Fg’s because we know the masses involved and g is always 9. 8 m/s 2. The problem is FT we don’t know what it is and we can not calculate it!? ! Lets get rid of it! Make a substitution

Substitute for FT n n n If m 2 a = m 2 g – FT, then FT = m 2 g – m 2 a Substitute m 2 g – m 2 a in for FT in Eqn 2. And get m 1 a = -m 1 g + m 2 g – m 2 a

Simplify m 1 a = -m 1 g + m 2 g – m 2 a + m 2 a n n m 1 a + m 2 a = -m 1 g + m 2 g Factor out the a’s and g’s a(m 1 + m 2) = g(-m 1 + m 2)

Solve for the acceleration a (m 1 + m 2) = g(-m 1 + m 2) ( m 1 + m 2)

Solve for the acceleration a = g (-m 1 + m 2) ( m 1 + m 2) OR a = g ( m 2 - m 1) ( m 1 + m 2)

Therefore a = g ( m 2 - m 1) ( m 1 + m 2) n Therefore we can compare our calculation from the above equation to the actual acceleration from our graph to determine the validity of Newton’s 2 nd Law!