A mouse pushes a piece of cheese with a mass of 6.4 g for a distance of 75 cm over a frictionless surface. He exerts a constant 0.5 N force as he does so. If the cheese starts from rest, what is it's final velocity?
78.125 m/s^2
To find the final velocity of the cheese, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, since the surface is frictionless, the only force acting on the cheese is the force exerted by the mouse.
First, we need to convert the mass of the cheese to kilograms. Since 1 gram is equal to 0.001 kilograms, the mass of the cheese is 6.4 g * 0.001 kg/g = 0.0064 kg.
Next, we can use the formula f = m * a, where f is the force, m is the mass, and a is the acceleration. Rearranging the formula, we can solve for acceleration:
a = f / m
Substituting the given values, we have:
a = 0.5 N / 0.0064 kg
Calculating this, we find that the acceleration of the cheese is approximately 78.13 m/s².
To find the final velocity, we can use the equation v² = u² + 2as, where v is the final velocity, u is the initial velocity (which is 0 since the cheese starts from rest), a is the acceleration, and s is the distance traveled.
Rearranging the equation, we can solve for v:
v² = 0² + 2 * 78.13 m/s² * 0.75 m
Simplifying this, we have:
v² = 2 * 58.595 m²/s²
v² ≈ 117.19 m²/s²
Taking the square root of both sides, we find:
v ≈ √(117.19 m²/s²)
v ≈ 10.82 m/s
Therefore, the final velocity of the cheese is approximately 10.82 m/s.