Hebelgesetz Aufgabe?
Hey,
ich habe eine Übungsaufgabe in Physik, und komme nicht weiter. Kann mir jemand helfen?
Aufgabenstellung: Am Ende einer drehbar gelagerten Stange der Länge 40 cm hängt eine Masse m, wie in der Abbildung dargestellt. Eine Feder mit einer Federkonstanten k = 200 N/m hält die Stange in der Waagerechten; sie ist in einem Abstand von 10 cm vom Drehzentrum befestigt. Die Feder ist 2 cm länger als im unbelasteten Zustand. Wie gross ist die Masse m? (g = 10 m/s2)
Vielen Dank 🙂
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You can be glad that there is no spring rest length. This would mean that you would also have to calculate the lateral deflection of the spring as a result of the rotational movement. Then you’d go to the floor. This is expected, for example, by mechanical engineering students.
It’s easy here. You just need to consider two laws:
Spring force = spring constant * spring deflection
and the leverage law:
Force1 + lever arm1 = Force2 + lever arm2
And of course Weight force = mass * g
First of all, you have to calculate the force acting on the spring. You can use the following formula:
F = D = s
Here is:
So you simply convert 2 cm in meters and put the values in the formula.
To get to the mass, you only need the weight force of m. Here the force transducer comes into play: the potential energy of the spring and the mass m are in equilibrium. You know the force acting on the spring, 10 cm from the center of gravity. So how much force must act on the mass m, which is 4 times as far away from the pivot point as the spring?
If you know the weight force of the mass m, you just need to put it in the formula
F = m • g
and change to m. For g, you can use 10 m/s2 according to the task.
Spring force = 200 N/m * 0.02 m = 4 N
Leverage
Fg * 40 cm = 4 N * 10 cm
Fg = 1 N
Fg = m*g
m = Fg/g = 0.1 kg = 100g
LG H.