Two ice fisherman stand face to face on the ice. They put their hands together, and push away from each other. The first man, who has a mass of 75 kg, accelerates backwards at 3.1 m/s What is the acceleration of the other man, who weigh 637N?
To find the acceleration of the other man, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's convert the weight of the other man from newtons to kilograms. We can do this by dividing the weight (637N) by the acceleration due to gravity (9.8 m/s^2):
Weight = mass × acceleration due to gravity
637N = mass × 9.8 m/s^2
Rearranging the equation and solving for mass:
mass = 637N / 9.8 m/s^2 = 65 kg
Now we can use the information given about the first man to find the acceleration of the other man. We know that the first man, with a mass of 75 kg, accelerates backwards at 3.1 m/s. Since the two fishermen are pushing against each other with equal and opposite forces, we can assume that the forces acting on them are the same magnitude.
Using Newton's second law, we can set up the following equation:
Force_1 = mass_1 × acceleration_1 = mass_2 × acceleration_2
Substituting the given values:
75 kg × 3.1 m/s = 65 kg × acceleration_2
Solving for acceleration_2:
acceleration_2 = (75 kg × 3.1 m/s) / 65 kg
acceleration_2 ≈ 3.57 m/s
So, the acceleration of the other man is approximately 3.57 m/s.