Three forces
F1 = (80.90i − 54.63j) N,
F2 = (23.50i − 80.52j) N,
and
F3 = (−104.4i + 361.9j) N
are exerted on a particle. The particle's mass is 23.11 kg. Find the particle's acceleration. (Express your answer in vector form.)
a =
m/s2
"physic
[fiz-ik]
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noun
1.
a medicine that purges; cathartic; laxative.
2.
any medicine; a drug or medicament.
3.
Archaic. the medical art or profession.
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find each vector acceleration: force/mass
then add them by adding like components.
Or, you can add the three forces, then divide by mass.
Ftotal/m-->(0i+226.75j)N/23.11kg=0i+9.81j m/s^2
To find the particle's acceleration, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
First, let's find the net force acting on the particle by summing up the individual forces. Given that:
F1 = (80.90i - 54.63j) N,
F2 = (23.50i - 80.52j) N,
F3 = (-104.4i + 361.9j) N,
To calculate the net force, we add the individual forces together:
Net Force = F1 + F2 + F3
Net Force = (80.90i - 54.63j) N + (23.50i - 80.52j) N + (-104.4i + 361.9j) N
Simplifying the equation, we can combine the i and j components separately:
Net Force = (80.90 + 23.50 - 104.4)i + (-54.63 - 80.52 + 361.9)j
Net Force = 0.00i + 227.75j N
Now, we have the net force acting on the particle. According to Newton's second law, we can calculate the acceleration by dividing the net force by the mass of the particle:
a = Net Force / Mass
Given that the mass of the particle is 23.11 kg, we substitute the values into the equation:
a = (0.00i + 227.75j N) / 23.11 kg
Now, we divide each component of the force by the mass:
a = (0.00i / 23.11 kg) + (227.75j N / 23.11 kg)
Simplifying the equation, we get:
a = 0.00i + 9.859j m/s^2
Therefore, the particle's acceleration in vector form is:
a = (0.00i + 9.859j) m/s^2