Question

1. Ralph drops a 0.040 kg racquetball from a 2^nd floor balcony. It falls 3.0 m in 0.85 seconds. Air resistance may affect the racquetball.

1. Calculate its impact velocity, assuming that its acceleration is constant.
2. Use energy methods to determine whether air resistance had a significant effect on the racquetball.

Answer 1

given :

m = mass = 0.04 kg

h = distance fall = 3 m

t = time spent = 0.85 s

initial velocity = u = 0

Let velocity after 0.85 s be v.

Let acceleration be a.

Using kinematic equation :

.

The calculated acceleration is less than acceleration due to gravity, it is due to the aire resistance on the ball.

a) The velocity of ball after this fall (i.e; after 0.85 s) is v = u + at = 0 + 8.30*0.85 = 7.06 m/s [answer]

b) Poetial energy of the ball at start of motion = mgh = 0.04*9.81*3 = 1.18 J [Total energy at start]

Using Work Energy Principle :

Work done by gravity + work done by air resistance = final kinetic energy - initial kinetic energy

.

The air resistance had significant effect on the ball, because there is loss of 0.18 J in energy due to air resistance as compared to total energy 1.18 J, which cannot be ignored.