Calculate the power output of a 1.7g spider as it walks up a windowpane at 2.5cm/s . The spider walks on a path that is at 25 ∘ to the vertical.
To calculate the power output of the spider, we need to use the formula:
Power = Force × Velocity
First, let's determine the force exerted by the spider. The force can be calculated using Newton's second law:
Force = Mass × Acceleration
Since the spider is walking on a path that is at an angle of 25 degrees to the vertical, we need to consider the vertical component of the force. The vertical component of acceleration is given by:
Acceleration = g × sin(θ)
Where:
g = acceleration due to gravity = 9.8 m/s^2 (approximately)
θ = angle of the path to the vertical = 25 degrees
So, the vertical component of acceleration is:
Acceleration = 9.8 m/s^2 × sin(25°)
Next, we need to calculate the vertical component of force exerted by the spider, which can be determined using the equation:
Force = Mass × Acceleration
Given that the mass of the spider is 1.7g = 1.7 × 10^-3 kg, we can substitute the values to find the vertical component of force.
Now, let's calculate the velocity of the spider in meters per second since Power = Force × Velocity. The given velocity is 2.5 cm/s. We need to convert this to meters per second by dividing by 100.
Finally, use the calculated force (vertical component) and velocity to determine the power output by substituting the values into the Power formula.
I'll calculate the results: