A mass is being pulled forward at a constant velocity of 3 m/s with a force of 15 N. The weight of the mass is 9.0 N.
What applied force must be exerted so that the mass will accelerate to 14 m/s in 4.0 seconds.
*Another one I don't understand. I even tried converting the newtons and still nothing.
yup
mass = 9/g = 9/9.81 kg = .917
friction or other force holding it back = 15 Newtons
so
F - 15 = ma = .917 (a)
but a = 14/4
so
F = 15 + .917(14/4)
= 18.2 N
To find the applied force required to accelerate the mass, we can use Newton's second law of motion. According to the second law, the force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
In this case, the mass (m) is not given, but we can use the weight (W) to find it. The weight of an object is the force due to gravity acting on it. So, we have:
W = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s²). Rearranging the equation will give us the mass:
m = W / g
Given that the weight (W) is 9.0 N, we can substitute the values into the equation:
m = 9.0 N / 9.8 m/s² ≈ 0.92 kg
Now, we can calculate the applied force (F) required to accelerate the mass. We know the final velocity (v) is 14 m/s, the initial velocity (u) is 3 m/s, and the time (t) is 4.0 seconds. The acceleration (a) can be calculated using the formula:
a = (v - u) / t
Substituting the given values:
a = (14 m/s - 3 m/s) / 4.0 s = 2.75 m/s²
Finally, we can find the applied force (F) using Newton's second law:
F = m * a = 0.92 kg * 2.75 m/s² ≈ 2.53 N
Therefore, the applied force that must be exerted to accelerate the mass to 14 m/s in 4.0 seconds is approximately 2.53 N.