Find the magnitude of the acceleration of the particle.

In summary, the question is asking to find the acceleration of a particle with an unknown mass m, placed between two fixed masses of 8.50 kg and 13.5 kg, held 50.0 cm apart. Using the formula for gravitational force, the magnitude of the force acting on the particle is calculated to be 1.2246*10^-7 N. However, the question is actually asking for the acceleration of the particle, not the force between the two fixed masses. By considering the net force acting on the particle and using the formula for acceleration, the final answer is found to be 6.37*10^-9 m/s^2.
  • #1
saturn67
54
0
An 8.50 kg point mass and a 13.5 kg point mass are held in place 50.0 cm apart. A particle of mass m is released from a point between the two masses 19.0 cm from the 8.50 kg mass along the line connecting the two fixed masses.

Find the magnitude of the acceleration of the particle.

Fg=(Gm1m2)/r^2


G=6.67*10^-11
m1=8.50kg
m2=13.5
r=(50/2)/100=.25m

so Fg =((6.67*10^-11)*8.50*13.5)/(.25^2)
Fg=1.2246*10^-7

F=ma since particle close to 8.5kg
a= 1.2246*10^-7/8.50
=1.440*10^-8 m/s^2

why this answer wrong please help me
 
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  • #2
You seem to be trying to calculate the force that exists between the 8.5 and the 13.5 kg masses (although the distance between them is 0.5 not .25m). But this question is really about mass m.


mass m is being pulled by two different forces...one from the 8.5 kg mass and the other from the 13.5 kg mass. It may help to draw a free body diagram of mass m and then write a net force equation for it. It is this net force that is responsible for the acceleration.
 
Last edited:
  • #3
so Fg =((6.67*10^-11)*8.50*13.5)/(.5^2) = 3.6018*^-9 N

Fnet = F2+F1= F(m2+m1)

so a= Fg/(m2+m1) ?
 
  • #4
bump, is this equation right

a= Fg/(m2+m1)
 
  • #5
I figured it outyou take ((G)(8.5)(m))/(.19m)^2
=1.57E-8 m

then you take ((G)(13.5)(m))/(.31m)^2
=9.37E-9 m

now just subtract the bottom one from the top to get your acceleration.
 

What is the definition of acceleration?

Acceleration is the rate of change of velocity over time. It is a vector quantity, meaning it has both magnitude and direction.

How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. The equation for acceleration is a = (v2 - v1)/t, where v2 is the final velocity, v1 is the initial velocity, and t is the change in time.

What is the difference between average and instantaneous acceleration?

Average acceleration is the overall change in velocity over a period of time, while instantaneous acceleration is the acceleration at a specific moment in time.

How does acceleration affect an object's motion?

Acceleration can change the speed, direction, or both of an object's motion. If there is no acceleration, an object will continue moving at a constant velocity.

How is acceleration related to force?

According to Newton's second law of motion, force is directly proportional to acceleration. This means that the greater the force applied to an object, the greater its acceleration will be.

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