I have been out of school 27 years; no Algebra or Trigonometry training: only remedial math.
This class is part of a Diploma program, no placement test required - I am out of my depth.
I had a tutor for an hour last Tues., with another appt. this Tues.
Yet, like I told my instructor; I am years too far behind.
I just need to know what are the correct formulas and steps to use for problems like these:
What is the momentum of a hammer of mass 0.8kg striking a nail at 5 m/s2?
So, p = m v
p = (0.8)(5 m/s)2
p = 20 kg-m/s2
Correct?
A nail stops the hammer in 0.08 seconds: what force is delivered to the nail?
Force is mass times gravity?
So, F = (0.8kg) (9.8 m/s2)
F = (0.8) (9.8)2
F = 76.832 N?
Am I on the right path?
What is the momentum of a hammer of mass 0.8kg striking a nail at 5 m/s2?
So, p = m v
p = (0.8)(5 m/s)
p = 4 kg-m/s note velocity is meters/seconds, acceleration is m/s^2
A nail stops the hammer in 0.08 seconds: what force is delivered to the nail?
NEWTON #2 Force = rate of change of momentum (m a)
F = p/t = 4 kg m/s / .08 s
F = 50 N
Yes, you're on the right path! Let's break down each question step by step.
1. Momentum of the hammer:
The momentum of an object is given by the formula p = m*v, where p is momentum, m is mass, and v is velocity. You correctly used the formula. Given the mass of the hammer as 0.8 kg and the velocity as 5 m/s, you multiplied these values together to get the momentum.
p = (0.8 kg)*(5 m/s)
p = 4 kg*m/s
So, the momentum of the hammer is 4 kg*m/s.
2. Force delivered to the nail:
To calculate the force delivered to the nail, we need to use another formula. Force is equal to the rate of change of momentum, which can be expressed as F = Δp/Δt. In this case, since the nail stops the hammer, the change in momentum is equal to the initial momentum of the hammer.
Now, we know that the hammer's momentum is 4 kg*m/s, and it stops in 0.08 seconds. We will assume gravity is not relevant in this context since the force is delivered by the hammer's impact. Therefore, we do not need to use the formula F = m*g.
F = (4 kg*m/s) / (0.08 s)
F = 50 N
So, the force delivered to the nail is 50 Newtons.
In summary, you correctly applied the formulas for these problems, and your calculations are accurate. Keep in mind that understanding the concepts behind the formulas and practicing additional problems can help you gain confidence and strengthen your math skills.