Why Does a Smaller Mass Reach the End of a Frictionless Track First?

In summary, on a frictionless track, two objects with different masses but equal forces applied to them will reach the end at different times. This is because the smaller mass will have a greater acceleration due to the same force, leading to a higher velocity and faster travel time. This can be explained by Newton's Second Law and the equation v=√2(F/m)Δx, which shows that for a given distance, velocity is inversely proportional to mass.
  • #1
Q7heng
10
0

Homework Statement


Hi, on my recent test there was a question stating 2 objects, one with a mass of m, and another with a mass of 4m, are pushed with equal forces on a frictionless track. The question asked which object will reach the end first and I said they will reach at the same time because there is no friction. But the right answer is the smaller mass will reach there first. I don't know how this works into everything in the equations of physics and how force, mass and velocity (not acceleration) is related. Help please!

Homework Equations


F=ma

Thanks a lot
 
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  • #2
You know how force relates to mass and acceleration. Which mass will have the greater acceleration?
How does velocity depend on acceleration?
 
  • #3
Shouldn't acceleration be 0 in this case because there is no friction on track?
 
  • #4
Q7heng said:
Shouldn't acceleration be 0 in this case because there is no friction on track?
I have no idea why you would think that.
Acceleration results from a nonzero net force. If there is an applied force and nothing to oppose it then there will be acceleration.
Indeed, there is less likely to be acceleration when there is friction.
 
  • #5
Q7heng said:
Shouldn't acceleration be 0 in this case because there is no friction on track?

That would be the case if they were coasting down the track. However the question as written in post #1 states they are being pushed down the track by a force.
 
  • #6
∑Fx=ma (Newton's Second Law)

F(Push)=ma The only force acting in the direction of motion is the push.

We can also write Newton's second law for the y-direction, but it doesn't tell us anything. ∑Fy=N-mg=0 →N=mg.

Back to the x-direction, we found that a=F(Push)/m by solving Newton's second law in the x-direction for a.

Now we can use kinematics. Since distance is implicitly given, I would use the equation,

v2=2a(xf-xi)=2aΔx

So,

v=√2aΔx or v=√2(F/m)Δx

since m is on the bottom, for a given Δx (i.e. the length of the track) v gets larger as m gets smaller
 

FAQ: Why Does a Smaller Mass Reach the End of a Frictionless Track First?

What is the relationship between force and velocity?

The relationship between force and velocity is described by Newton's second law of motion, which states that the force applied on an object is directly proportional to its mass and acceleration. In other words, the greater the force applied on an object, the greater its acceleration will be, and therefore its velocity will also increase.

How does force affect an object's velocity?

The force applied on an object directly affects its velocity by changing its acceleration. If a force is applied in the same direction as the object's velocity, it will increase the object's speed. On the other hand, if the force is applied in the opposite direction, it will decrease the object's speed and eventually stop it.

Can an object's velocity change without a force being applied?

No, an object's velocity cannot change without a force being applied. According to Newton's first law of motion, an object will remain at rest or in constant motion in a straight line at a constant speed unless acted upon by an external force. Therefore, a change in velocity requires a force to be applied to the object.

How is force related to the mass of an object?

The force applied on an object is directly proportional to its mass. This means that the greater the mass of an object, the greater the force needed to accelerate it at a given rate. This relationship is described by the equation F=ma, where F is the force, m is the mass, and a is the acceleration.

What is the unit of measurement for force and velocity?

Force is typically measured in Newtons (N) while velocity is measured in meters per second (m/s). However, other units of force and velocity may also be used, such as pounds (lb) and feet per second (ft/s), respectively. It is important to use consistent units when solving problems involving force and velocity to ensure accurate calculations.

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