A track of mass 1000 kg travelling on a straight level road accelerates from a speed of 10 m/s to a speed of 30 m/s in 12 seconds. Given that the engine of the track exerts a constant pull of magnitude P N and that there is a constant resistance to motion of 200 N, find the value of P.
v changed from 10 to 30 in 12 sec.
So, the acceleration
a = 20/12 = 5/3 m/s^2
F = ma = 1000*5/3 = 1667 N
That is the net force, and since there is an opposing force of 200N,
P = 1667+200 = 1867 N
To find the value of P, we can use Newton's second law of motion.
According to Newton's second law, the net force (F_net) applied to an object is equal to the product of its mass (m) and its acceleration (a).
F_net = m * a
In this case, the net force is the difference between the force applied by the engine (P) and the resistance to motion (200 N).
F_net = P - 200
The acceleration is given as the change in velocity (Δv) divided by the time taken (t).
a = Δv / t
We are given the initial velocity (u = 10 m/s), final velocity (v = 30 m/s), and the time taken (t = 12 s). We can calculate the change in velocity as follows:
Δv = v - u
Δv = 30 m/s - 10 m/s
Δv = 20 m/s
Now, substituting the values into the equation, we get:
a = 20 m/s / 12 s
a ≈ 1.67 m/s²
Substituting the values of acceleration and net force equation into Newton's second law equation:
P - 200 = m * a
P - 200 = 1000 kg * 1.67 m/s²
P ≈ 1000 kg * 1.67 m/s² + 200
P ≈ 1670 N + 200
P ≈ 1870 N
Therefore, the value of P is approximately 1870 N.
To find the value of P, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
We know the mass of the track is 1000 kg and the initial speed is 10 m/s. The final speed is 30 m/s. The time taken is 12 seconds.
First, let's calculate the acceleration of the track:
Acceleration (a) = (final velocity - initial velocity) / time
= (30 m/s - 10 m/s) / 12 s
= 20 m/s / 12 s
= 5/3 m/s^2
Now, let's calculate the net force acting on the track:
Net force = mass * acceleration
= 1000 kg * (5/3 m/s^2)
= 5000/3 N
The net force consists of two components: the force exerted by the engine (P) and the resistance to motion (200 N). Therefore, we can write the equation as:
P - 200 N = 5000/3 N
Now, let's solve for P:
P = 5000/3 N + 200 N
P = 5000/3 N + 600/3 N
P = (5000 + 600)/3 N
P = 5600/3 N
P ≈ 1866.67 N
Therefore, the value of P is approximately 1866.67 N.