A large block P executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency f = 1.7 Hz. Block B rests on it, as shown in the figure, and the coefficient of static friction between the two is ìs=0.64. (b) What is the maximum force of static friction for a 6.7 kg mass?
friction=mu*massB*g
you are given massB, mu, and you should know g.
The wording here is a bit suspicious. Maximum acceleration occurs when the amplitude is maximum, and it is acceleration=-(2PI*f)^2*maxAmplitude
so when you know the maxAmplitude, you can figure acceleration, which is of course force=mass*acceleration, and the force on the block B is that force. If it is greater than friction, the block slides off.
To find the maximum force of static friction between block P and block B, we need to consider the maximum force that can be exerted without causing the blocks to move. This occurs when the force of static friction reaches its maximum value, equal to the product of the coefficient of static friction and the normal force.
First, let's find the normal force acting on block B. The normal force is the force exerted by the surface of block P on block B, perpendicular to the contact surface.
The weight of block B is given by its mass m multiplied by the acceleration due to gravity g:
Weight of block B = m * g
Using the given mass of 6.7 kg and the acceleration due to gravity of approximately 9.8 m/s^2, we can find the weight of block B:
Weight of block B = 6.7 kg * 9.8 m/s^2
Next, we need to find the normal force between block P and block B. Since the surfaces are in contact, the normal force is equal in magnitude and opposite in direction to the weight of block B. Therefore, the normal force is:
Normal force = Weight of block B
Now that we have the normal force, we can find the maximum force of static friction using the equation:
Maximum force of static friction = coefficient of static friction * Normal force
Given that the coefficient of static friction is 0.64, we substitute the values into the equation:
Maximum force of static friction = 0.64 * (Weight of block B)
Finally, we substitute the weight of block B value we calculated earlier into the equation:
Maximum force of static friction = 0.64 * (6.7 kg * 9.8 m/s^2)
Now, we can perform the calculation to find the maximum force of static friction for a 6.7 kg mass.