The system shown below are in equilibrium with m = 2.90 kg If the spring scales are calibrated in newtons, what do they read? Ignore the masses of the pulleys and strings and assume the pulleys and the incline are frictionless.
Image: imgur. com/a/GCJIL
2.9*9.81 Newtons
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To determine the readings on the spring scales, we need to consider the forces acting on the system. In this case, we have an inclined plane with masses on either side of a pulley. Let's break it down step by step:
1. Start by drawing a free-body diagram for each mass. The diagram should show all the forces acting on each mass separately.
2. For the 2.90 kg mass on the inclined plane, there are two forces acting: the weight force mg (directed straight downwards) and the normal force N (perpendicular to the contact surface of the inclined plane).
3. Resolve the weight force into components. Since the inclined plane is at an angle, the component of the weight force acting parallel to the plane is mg*sin(theta), and the component perpendicular to the plane is mg*cos(theta). (Here, theta is the angle of inclination of the plane.)
4. Now consider the other mass hanging vertically. The only force acting on it is its weight mg straight downwards.
5. Next, consider the tension in the string. Since the string is connected to both masses and passes over a pulley, it exerts the same tension on both sides of the pulley.
6. Apply Newton's second law, F = ma, to the two masses separately. In the case of the mass on the inclined plane, the net force in the direction parallel to the plane is T - mg*sin(theta), and in the perpendicular direction, it is N - mg*cos(theta). For the hanging mass, the net force is T - mg.
7. Since the system is in equilibrium, the net force on each mass in the perpendicular direction must be zero (N - mg*cos(theta) = 0). Also, the net force parallel to the plane for the mass on the inclined plane and the hanging mass must be zero (T - mg*sin(theta) = 0 and T - mg = 0).
8. From these equations, we find that N = mg*cos(theta), T = mg*sin(theta), and T = mg.
9. Now, you can calculate the readings on the spring scales. Since T = mg, the reading on each spring scale will be equal to the gravitational force acting on each mass. Therefore, the reading on each scale will be m*g, where m is the mass given (2.90 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
To summarize, the readings on the spring scales will be 2.90 kg * 9.8 m/s^2 = 28.42 N.