A force of 80.0 N is required to pull a 25.0 kg wooden toy boat at a constant velocity across a smooth glass surface on Earth. What force would be required to pull the same wooden toy boat across the same glass surface on the planet Jupiter?
To find the force required to pull the wooden toy boat across the glass surface on Jupiter, we need to consider the difference in gravitational force between Earth and Jupiter.
The force required to pull the wooden toy boat on Earth is the force of friction between the boat and the glass surface. This force can be calculated using the equation:
Force of friction = coefficient of friction * normal force
On Earth, the normal force is equal to the weight of the wooden toy boat. The weight can be calculated using the formula:
Weight = mass * gravitational acceleration
Where the mass of the wooden toy boat is 25.0 kg and the gravitational acceleration on Earth is approximately 9.8 m/s².
Therefore, the weight of the wooden toy boat on Earth is:
Weight = 25.0 kg * 9.8 m/s² = 245.0 N
Since the force of friction required to pull the boat on Earth is 80.0 N, we can write:
80.0 N = coefficient of friction * 245.0 N
Dividing both sides by 245.0 N gives:
coefficient of friction = 80.0 N / 245.0 N ≈ 0.327
Now, to find the force required to pull the wooden toy boat on Jupiter, we need to calculate the gravitational force and the normal force on Jupiter.
The gravitational acceleration on Jupiter is approximately 24.8 m/s². So, the weight of the wooden toy boat on Jupiter can be calculated as:
Weight on Jupiter = mass * gravitational acceleration on Jupiter
Substituting the values, we have:
Weight on Jupiter = 25.0 kg * 24.8 m/s² = 620.0 N
Since we already know the coefficient of friction (0.327), we can now find the force of friction required to pull the wooden toy boat on Jupiter:
Force of friction on Jupiter = coefficient of friction * normal force on Jupiter
Substituting the values, we have:
Force of friction on Jupiter = 0.327 * 620.0 N
Simplifying the equation, we get:
Force of friction on Jupiter ≈ 202.54 N
Therefore, the force required to pull the same wooden toy boat across the same glass surface on Jupiter would be approximately 202.54 Newtons.