A honeybee with a mass of 0.175 g lands on one end of a popsicle stick (Active Example 9-2). After sitting at rest for a moment, the bee runs toward the other end with a velocity 1.75 cm/s relative to the still water. What is the speed of the 5.00 g stick relative to the water? (Assume the bee's motion is in the negative direction.)
To find the speed of the stick relative to the water, we need to consider the conservation of momentum.
The momentum of an object is given by the product of its mass and velocity.
First, let's find the momentum of the bee.
Momentum of the bee = mass of the bee × velocity of the bee
Given:
Mass of the bee = 0.175 g = 0.175 grams = 0.175 × 10^(-3) kg (converting from grams to kilograms)
Velocity of the bee = 1.75 cm/s = 1.75 × 10^(-2) m/s (converting from centimeters to meters)
Momentum of the bee = (0.175 × 10^(-3) kg) × (1.75 × 10^(-2) m/s)
Next, let's find the momentum of the stick. Since the stick is initially at rest, its momentum is zero.
Momentum of the stick = 0 kg × velocity of the stick
Now, let's find the speed of the stick relative to the water, which can be understood as the velocity of the stick.
Total momentum before the bee started running = Total momentum after the bee started running
Momentum of the bee = Momentum of the stick
(0.175 × 10^(-3) kg) × (1.75 × 10^(-2) m/s) = 0 kg × velocity of the stick
Simplifying the equation:
(0.175 × 10^(-3) kg) × (1.75 × 10^(-2) m/s) = 0 kg × velocity of the stick
0.0030625 kg·m/s = 0 kg × velocity of the stick
Since the mass of the stick is 5.00 g = 5.00 × 10^(-3) kg (converting from grams to kilograms), we can rewrite the equation as:
0.0030625 kg·m/s = (5.00 × 10^(-3) kg) × velocity of the stick
Simplifying further:
0.0030625 kg·m/s = 0.005 kg × velocity of the stick
To find the velocity of the stick, divide both sides of the equation by 0.005 kg:
velocity of the stick = (0.0030625 kg·m/s) ÷ (0.005 kg)
Simplifying:
velocity of the stick = 0.6125 m/s
Therefore, the speed of the 5.00 g stick relative to the water is 0.6125 m/s.