A tractor pulls a loaded wagon with a constant force of 300 N. If the total mass of the wagon and its contents is 275 kg, (a) what is the wagon's acceleration? (b) Assuming the wagon started from rest, how far does the tractor travel in 4.00 s?
If there is no retarding force, then
net force=m*a
pulling force-retarding force=ma
300-0=275*a solve for a
distancethen=a*time
To find the wagon's acceleration, we can use Newton's second law of motion: F = ma, where F is the applied force, m is the mass, and a is the acceleration.
(a) In this case, the applied force is 300 N and the total mass of the wagon and its contents is 275 kg. So we have:
F = ma
300 N = (275 kg) * a
To find the acceleration, we can rearrange the equation:
a = (300 N) / (275 kg)
a ≈ 1.091 m/s^2
Therefore, the wagon's acceleration is approximately 1.091 m/s^2.
(b) Assuming the wagon started from rest, we can use the equation of motion: d = (1/2) * a * t^2, where d is the distance, a is the acceleration, and t is the time.
In this case, the acceleration is 1.091 m/s^2 and the time is 4.00 s. So we have:
d = (1/2) * (1.091 m/s^2) * (4.00 s)^2
d = 0.5 * 1.091 m/s^2 * 16.00 s^2
d ≈ 8.728 m
Therefore, the tractor travels approximately 8.728 meters in 4.00 seconds.
To answer these questions, we need to apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
(a) To find the wagon's acceleration, we can use the formula:
acceleration = net force / mass
Given that the force applied by the tractor is 300 N and the total mass of the wagon and its contents is 275 kg, we can substitute these values into the formula:
acceleration = 300 N / 275 kg
By dividing these values, we get:
acceleration ≈ 1.09 m/s^2
Therefore, the wagon's acceleration is approximately 1.09 m/s^2.
(b) To find the distance traveled by the tractor in 4.00 s, we can use the equation of motion:
distance = initial velocity * time + (1/2) * acceleration * time^2
Since the wagon starts from rest, the initial velocity is zero. Therefore, the equation becomes:
distance = (1/2) * acceleration * time^2
Substituting the values of acceleration = 1.09 m/s^2 and time = 4.00 s into the equation, we have:
distance = (1/2) * 1.09 m/s^2 * (4.00 s)^2
Calculating the right side of the equation, we get:
distance ≈ 8.72 m
Therefore, the tractor travels approximately 8.72 meters in 4.00 seconds.