A girl pulls a toy train with a horizontal force of 10N The tention between the locomotive and the carrdge is 3N the friction on the carrydgers in and the mass of the locomotive and carrydge are 2 kg and 1kg respectively now calculate the acceleration of the toy train and the friction on the locomotive
To calculate the acceleration of the toy train, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Given:
Force applied by the girl (F) = 10N
Tension between the locomotive and carriage (T) = 3N
Mass of the locomotive (m1) = 2kg
Mass of the carriage (m2) = 1kg
First, let's find the net force acting on the train. The net force is equal to the force applied by the girl minus the force of tension between the locomotive and the carriage.
Net force (F_net) = F - T
F_net = 10N - 3N
F_net = 7N
Now, we can calculate the acceleration (a) using Newton's second law:
F_net = m1 * a
7N = 2kg * a
a = 7N / 2kg
a ≈ 3.5 m/s²
So, the acceleration of the toy train is approximately 3.5 m/s².
Next, let's determine the friction on the locomotive. The friction force can be found using the formula:
Friction force (F_friction) = μ * Normal force
Where μ is the coefficient of friction and it depends on the surfaces in contact, and the Normal force is the force exerted perpendicular to the surface.
Since the toy train is pulled horizontally, the normal force between the locomotive and the surface is equal to the weight of the locomotive.
Mass of the locomotive (m1) = 2kg
Acceleration due to gravity (g) = 9.8 m/s²
Weight of the locomotive (W) = m1 * g
W = 2kg * 9.8 m/s²
W = 19.6N
Let's assume the coefficient of friction (μ) between the locomotive and the surface is 0.2.
F_friction = μ * W
F_friction = 0.2 * 19.6N
F_friction = 3.92N
Therefore, the friction on the locomotive is approximately 3.92N.
To calculate the acceleration of the toy train, we can use Newton's second law of motion, which states that the force applied is equal to the mass of the object multiplied by its acceleration.
Given:
Force applied (F) = 10N
Mass of the locomotive (m1) = 2kg
Mass of the carriage (m2) = 1kg
Since the force applied is in the horizontal direction and there is no vertical component, we can assume that the tension between the locomotive and the carriage will cancel out. Therefore, the net force acting on the toy train is equal to the force applied minus the friction force.
To calculate the net force:
Net Force (Fnet) = Force applied (F) - Friction force
Now, let's calculate the friction force:
Friction force (Ff) = μ * Normal force
The normal force is the perpendicular force exerted by a surface to support the weight of an object resting on it. In this case, since the toy train is on a horizontal surface, the normal force is equal in magnitude but opposite in direction to the force of gravity acting on the toy train.
Normal force (N) = Weight (W) = mass * gravitational acceleration (g)
Given:
Gravitational acceleration (g) ≈ 9.8 m/s^2
Now, let's calculate the normal force and subsequently the friction force:
Weight (W) = (m1 + m2) * g
Normal force (N) = Weight (W)
Once we have the normal force, we can find the friction force using the coefficient of friction (μ) and the equation mentioned earlier.
Now, with the friction force known, we can calculate the net force acting on the toy train:
Fnet = F - Ff
Finally, we can calculate the acceleration (a) of the toy train using Newton's second law equation:
a = Fnet / (m1 + m2)
To summarize, the steps are as follows:
1. Calculate the weight (W) of the toy train.
2. Calculate the normal force (N) using W.
3. Calculate the friction force (Ff) using μ * N.
4. Calculate the net force (Fnet) using F - Ff.
5. Calculate the acceleration (a) using Fnet / (m1 + m2).
Please provide the value of the coefficient of friction (μ) in order to proceed with calculations.