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?
there is no time or speed givin, which throws me off
To find the final velocity of the cheese, we can use the equation:
Work = Change in kinetic energy
Since the surface is frictionless, the work done by the mouse is equal to the change in kinetic energy of the cheese. The work done can be calculated using the formula:
Work = Force * Distance
Here, the force applied by the mouse is 0.5 N and the distance traveled by the cheese is 75 cm (0.75 m). Therefore, the work done is:
Work = 0.5 N * 0.75 m = 0.375 J
Now, let's consider the change in kinetic energy. Since the cheese starts from rest, its initial kinetic energy is zero. The final kinetic energy can be calculated using the equation:
Change in kinetic energy = 0.5 * Mass * Final velocity^2
Here, the mass of the cheese is 6.4 g (0.0064 kg) and the final velocity is what we need to find. Rearranging the equation, we get:
Final velocity^2 = (2 * Change in kinetic energy) / Mass
Final velocity^2 = (2 * 0.375 J) / 0.0064 kg
Final velocity^2 ≈ 46.875 m^2/s^2
Finally, we can find the final velocity by taking the square root of both sides:
Final velocity ≈ √46.875 m^2/s^2
Final velocity ≈ 6.855 m/s
Therefore, the final velocity of the cheese is approximately 6.855 m/s.
To find the final velocity of the cheese, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied on it and inversely proportional to its mass.
First, let's check if the given information is sufficient. The mass of the cheese, its distance traveled, and the applied force are provided, but the time is not mentioned. However, we can solve for time using other information.
We know that the mouse exerts a constant force of 0.5 N on the cheese. The force applied can be related to the acceleration of the cheese using Newton's second law:
F = ma
Where:
F is the force applied (0.5 N),
m is the mass of the cheese (6.4 g or 0.0064 kg),
and a is the acceleration of the cheese.
Rearranging the equation, we have:
a = F / m
Substituting the given values:
a = 0.5 N / 0.0064 kg
a ≈ 78.125 m/s²
Now, we need to find the time it takes for the cheese to travel a distance of 75 cm (or 0.75 m). The equation to calculate the final velocity is:
v = u + at
Where:
v is the final velocity,
u is the initial velocity (which is 0 m/s since the cheese starts from rest),
a is the acceleration calculated previously,
and t is the time.
Rearranging the equation to solve for t, we have:
t = (v - u) / a
Substituting the given values and rearranging the equation, we get:
t = (0.75 m - 0 m) / 78.125 m/s²
t ≈ 0.0096 s
Now that we have calculated the time it takes for the cheese to travel a distance of 75 cm, we can find the final velocity by substituting the values into the rearranged equation:
v = u + at
v = 0 m/s + (78.125 m/s²)(0.0096 s)
v ≈ 0.75 m/s
Therefore, the final velocity of the cheese is approximately 0.75 m/s.