Hi,
I've been having trouble with this physics problem. I'm not sure where to begin.
A brick with mass m1=2.5 kg can move without friction on a horizontal plane. The brick
is attached to a wall by an ideal spring with spring constant k=2300 N/m. A second brick
with mass m2=1.2 kg lies on top of the brick as shown in Fig. 4. The static coefficient of
friction between the bricks is µs=0.56.
a) Assuming that m2 does not slide on m1 calculate the period, T, of small angle
oscillations for this system.
b) Calculate the maximum amplitude of oscillation at which m2 can follow along
without beginning to slide on m1
Thanks in advance!
see
http://www.jiskha.com/display.cgi?id=1480442177
To solve this problem, we need to analyze the forces acting on the system and apply Newton's laws of motion.
a) To find the period of small angle oscillation, we can use the formula for the period of a mass-spring system, which is given by T = 2π√(m/k), where m is the mass attached to the spring and k is the spring constant.
In this case, the mass attached to the spring is the combined mass of m1 and m2, which we'll call M. So M = m1 + m2. The spring constant k is given as 2300 N/m.
To find the period T, we need to find the combined mass M. In this scenario, m2 does not slide on m1, implying there is enough static friction between the two bricks to ensure this. This means that the maximum horizontal force between the two bricks is given by the product of the normal force (N) and the static coefficient of friction (µs).
The normal force is the force exerted by the wall on the bottom brick, which is equal to the weight of the bottom brick since the system is at equilibrium. Using the equation N = m1 * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2), we can find the normal force.
The maximum horizontal force is also the force that the spring exerts on the bottom brick at maximum compression. This force is given by F = k * x, where x is the distance of compression.
Setting the maximum horizontal force equal to the product of the normal force and the static coefficient of friction, we have:
k * x = µs * m1 * g
Rearranging the equation, we can express the distance of compression x in terms of the given quantities:
x = (µs * m1 * g) / k
Substituting the values, we find the distance of compression x.
Now, substituting the values of M and k into the formula for the period T, we can find the answer to part a.
b) To calculate the maximum amplitude of oscillation at which m2 can follow along without beginning to slide on m1, we need to consider the limiting condition where the static friction between the two bricks is just sufficient to prevent sliding. In this case, the maximum amplitude occurs when the horizontal force between the bricks is equal to the product of the normal force and the static coefficient of friction.
The maximum horizontal force is again given by F = k * x, where x is the amplitude of oscillation.
Setting the maximum horizontal force equal to the product of the normal force and the static coefficient of friction, we have:
k * x = µs * m1 * g
Rearranging the equation, we can express the maximum amplitude x in terms of the given quantities:
x = (µs * m1 * g) / k
Substituting the values given, we can find the maximum amplitude x.
I hope this explanation helps you solve the problem! Let me know if you need any further assistance.