a mouse pushes a piece of cheese with a mass of 6.4 g for a distance of 75 cm over the frictionless surface of an air hockey table. He exerts a constant 0.5 N force as he does so. If the cheese starts from rest, what is it's final velocity?
Answer= 0.342327
To find the final velocity of the cheese, you can use the equation of motion:
v^2 = u^2 + 2as
Where:
- v is the final velocity
- u is the initial velocity (0 m/s, as the cheese starts from rest)
- a is the acceleration
- s is the distance traveled by the cheese
First, we need to find the acceleration (a) 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)
a = F / m
a = 0.5 N / 0.0064 kg
a ≈ 78.125 m/s^2
Now, we can substitute the known values into the equation of motion:
v^2 = 0^2 + 2 * 78.125 m/s^2 * 0.75 m
Simplifying:
v^2 = 0 + 117.1875 m^2/s^2
v ≈ √117.1875 m/s
v ≈ 10.82 m/s
Therefore, the final velocity of the cheese is approximately 10.82 m/s.
To find the final velocity of the cheese, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity (which is 0, since the cheese starts from rest)
a = acceleration
s = distance
First, let's find the acceleration. We can use Newton's second law of motion:
F = ma
Where:
F = force applied
m = mass of the cheese
a = acceleration
In this case, the force applied by the mouse is 0.5 N, and the mass of the cheese is 6.4 g (convert to kg):
6.4 g = 6.4 / 1000 kg = 0.0064 kg
Now we can find the acceleration:
a = F / m
= 0.5 N / 0.0064 kg
= 78.125 m/s^2
Next, let's find the distance in meters:
75 cm = 75 / 100 m = 0.75 m
Finally, we can calculate the final velocity:
v^2 = u^2 + 2as
= 0^2 + 2 * 78.125 m/s^2 * 0.75 m
= 117.1875 m^2/s^2
Taking the square root of both sides:
v = √(117.1875 m^2/s^2)
= 10.82 m/s
Therefore, the final velocity of the cheese is approximately 10.82 m/s.
F=ma
a=F/m
v=sqrt(2as)