A boxcar of mass 200 tons at rest becomes uncoupled on a 2.5 degree grade. If the track is considered to be frictionless, what speed does the boxcar have after 10 seconds?
I will be glad to critique your efforts. No one is showing any work.
I cant find the acceleration needed to solve the problem. All i know is 200tons is equal to 200000kg. and I don't understand 2.5 degree grade. would it be 200000cos2.5 ... but then how do i get acceleration from there.
To find the speed of the boxcar after 10 seconds, we can use the principles of physics, namely Newton's second law and the equations of motion. Let's break down the steps to solve the problem.
Step 1: Find the force acting on the boxcar.
Since the track is considered to be frictionless, the force acting on the boxcar is due to gravity only. We need to calculate the force acting down the inclined plane.
Force (F) = mass (m) * acceleration due to gravity (g)
Given: mass = 200 tons = 200,000 kg (since 1 ton = 1000 kg)
Acceleration due to gravity (g) = 9.8 m/s^2
F = 200,000 kg * 9.8 m/s^2 = 1,960,000 N
Step 2: Resolve the force into components.
The force acting on the boxcar can be resolved into two components: one along the incline and one perpendicular to it. The component acting along the incline will cause the acceleration of the boxcar.
Component of Force along the incline (F_parallel) = F * sin(θ)
θ is the angle of the grade, given as 2.5 degrees.
F_parallel = 1,960,000 N * sin(2.5 degrees)
Step 3: Calculate the acceleration of the boxcar.
The acceleration of the boxcar will be determined by the component of the force acting along the incline.
Acceleration (a) = F_parallel / mass
a = (1,960,000 N * sin(2.5 degrees)) / 200,000 kg
Step 4: Calculate the final velocity of the boxcar after 10 seconds.
We can use the equation of motion:
Final Velocity (v) = Initial Velocity (u) + (acceleration * time)
Given:
Initial Velocity (u) = 0 m/s (boxcar is at rest)
Time (t) = 10 seconds
v = 0 m/s + (a * t)
Compute the value of 'a' from Step 3 and substitute the values:
Final Velocity (v) = 0 m/s + [(1,960,000 N * sin(2.5 degrees)) / 200,000 kg] * 10 s
Simplify the equation and calculate the final velocity.
Final Velocity (v) ≈ [24.5 N/kg] * 10 s = 245 m/s
Therefore, the boxcar will have a speed of approximately 245 m/s after 10 seconds.