Ben pulls a rope that is attached to a wagon with a magnitude of 300N. He pulls it in a way that te rope is at an angle of 30 degrees from the horizontal. The mass of the wagon is 2kg and the mass of Mike, who sits on the wagon, is 20kg. While the wagon moves to the right, the friction acting on it has a magnitude of 50N. What is the magnitude of normal force acting on the wagon? What is the acceleration of the wagon?
To find the magnitude of the normal force acting on the wagon, we need to first find the net force acting on it in the vertical direction. Since the wagon is moving horizontally, the vertical acceleration is zero. Therefore, the net force in the vertical direction is also zero.
Since the only vertical force acting on the wagon is the weight of Mike, we can conclude that the magnitude of the normal force is equal to the weight of Mike. The weight of an object is given by the equation: weight = mass * acceleration due to gravity.
The mass of Mike is given as 20 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the magnitude of the normal force is:
Normal force = weight of Mike = mass of Mike * acceleration due to gravity
Normal force = 20 kg * 9.8 m/s^2 = 196 N
To find the acceleration of the wagon, we need to consider the net force acting on it in the horizontal direction. The horizontal force acting on the wagon is the force applied by Ben, minus the friction force.
The horizontal component of the pulling force applied by Ben can be found using trigonometry. The magnitude of the pulling force is given as 300 N, and the angle between the rope and the horizontal is 30 degrees. The horizontal component of the force can be found using the equation: horizontal component = force * cosine(angle).
Horizontal component = 300 N * cosine(30 degrees) ≈ 259.8 N
The net force acting on the wagon is the horizontal component of the pulling force minus the friction force:
Net force = horizontal component of pulling force - friction force
Net force = 259.8 N - 50 N = 209.8 N
Using Newton's second law of motion, which states that force equals mass times acceleration (F = ma), we can find the acceleration of the wagon:
209.8 N = (mass of wagon + mass of Mike) * acceleration
209.8 N = (2 kg + 20 kg) * acceleration
Simplifying the equation:
209.8 N = 22 kg * acceleration
acceleration = 209.8 N / 22 kg
acceleration ≈ 9.54 m/s^2
Therefore, the magnitude of the normal force acting on the wagon is 196 N, and the acceleration of the wagon is approximately 9.54 m/s^2.
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50N
4.5m/s^2