(Physics) Magnitude and Direction

Question

A string goes over a frictionless/massless pulley. At the end of each side of the rope are identical nuts of negligible mass. Two squirrels see the nuts at the same time and both lunge for the nuts. Squirrel 1 goes for the nut on the right and squirrel 2 goes for the nut on the left. The mass of squirrel 1 is 0.11kg and the mass of squirrel 2 is 0.13kg. The magnitude of the gravitational acceleration is 9.8 m/s2.

After drawing the FBDs for each squirrel,

A) what is the magnitude and direction of acceleration for squirrel 1?

Answer 1

The FBD's for each squirrel will involve drawing the vectors from the weights of each squirrel, and the tension in the rope. The tension that each squirrel experiences is equal to the weight of the other squirrel. So if we sum the forces for Squirrel 1, we get:

∑F = m₁ * a₁ = m₂*g - m₁*g, this is Newton's Second Law.

Therefore, a₁ = (1/m₁)*(m₂*g - m₁*g)

a₁ = (1/0.11 [kg])*(0.13[kg]*9.8 [m/s²] - 0.11 [kg]*9.8 [m/s²])

a₁ = 1.782 [m/s²]