How Much Force Does a Toy Locomotive Exert on a Caboose?

In summary, the problem involves a toy locomotive pulling a caboose with a frictional force acting on it. The train is accelerating forward at 3.4 m/s2 and the question asks for the magnitude of the force exerted by the locomotive on the caboose. Using the formula F = ma and taking into account the frictional force, the net force needed to accelerate the caboose is (2.1 + 1.7)(3.4) + 0.51, or 13.43 N. However, this approach is incorrect and a Free Body diagram should be used to accurately solve the problem.
  • #1
foxat
2
0
A 2.1 kg toy locomotive is pulling a 1.7 kg caboose. The frictional force of the track on the caboose is 0.51 N backward along the track. If the train is accelerating forward at 3.4 m/s2, what is the magnitude of the force exerted by the locomotive on the caboose?
 
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  • #2
foxat said:
A 2.1 kg toy locomotive is pulling a 1.7 kg caboose. The frictional force of the track on the caboose is 0.51 N backward along the track. If the train is accelerating forward at 3.4 m/s2, what is the magnitude of the force exerted by the locomotive on the caboose?
Hello foxat. Welcome to PF !

What have you tried?

Where are you stuck?

You must show an attempt, before we can help you. --- those are the rules here at PF.
 
  • #3
Thanks!

I have approached this problem by using total F = ma, which equals the force exerted by the locomotive on the caboose minus the frictional force. So ma = F of the locomotive - 0.51, and thus F of the locomotive = ma + 0.51. The answer i came up with is (2.1 + 1.7)(3.4) + 0.51, or 13.43 N. Am I approaching this the right way?
 
  • #4
foxat said:
Thanks!

I have approached this problem by using total F = ma, which equals the force exerted by the locomotive on the caboose minus the frictional force. So ma = F of the locomotive - 0.51, and thus F of the locomotive = ma + 0.51. The answer i came up with is (2.1 + 1.7)(3.4) + 0.51, or 13.43 N. Am I approaching this the right way?
No.

What net force is needed to accelerate the caboose at 3.4 m/s2 ?

Also, do you know about Free Body diagrams ?
 
  • #5


The magnitude of the force exerted by the locomotive on the caboose can be determined using Newton's Second Law, which states that the net force on an object is equal to its mass multiplied by its acceleration (F=ma). In this scenario, the net force on the caboose is the sum of the force exerted by the locomotive and the frictional force of the track, which is acting in the opposite direction. Therefore, we can set up the following equation:

F - 0.51 N = (1.7 kg)(3.4 m/s2)

Solving for F, we get:

F = (1.7 kg)(3.4 m/s2) + 0.51 N

F = 5.78 N + 0.51 N

F = 6.29 N

Therefore, the magnitude of the force exerted by the locomotive on the caboose is approximately 6.29 N. This force is necessary to overcome the frictional force and accelerate the caboose forward at 3.4 m/s2. It is important to consider both the mass and acceleration of the objects when determining the magnitude of the force exerted in a system.
 

Related to How Much Force Does a Toy Locomotive Exert on a Caboose?

1. What is the locomotive forces problem?

The locomotive forces problem is a phenomenon in physics where the force required to move a train or locomotive increases as the speed of the train increases. This is due to various factors, such as air resistance and friction between the train and the tracks.

2. What causes the locomotive forces problem?

The locomotive forces problem is caused by the resistance that a train experiences as it moves through its environment. This resistance can come from sources such as air resistance, rolling resistance from the train's wheels, and the gradient of the tracks.

3. How does the locomotive forces problem affect train travel?

The locomotive forces problem can significantly impact the efficiency and speed of train travel. As the force required to move the train increases, it becomes more challenging to maintain high speeds and can lead to delays and increased energy consumption.

4. Is there a way to reduce the impact of the locomotive forces problem?

Yes, there are various methods used to reduce the impact of the locomotive forces problem. These include aerodynamic design of trains, using smoother and more level tracks, and implementing regenerative braking systems that can help reduce energy consumption.

5. How do scientists study the locomotive forces problem?

Scientists study the locomotive forces problem through various methods, including experiments, computer simulations, and mathematical models. They also gather data from real-world train travel to analyze and understand the factors that contribute to this phenomenon.

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