A block of mass m1 = 4.80 kg sits on top of a second block of mass m2 = 15.6 kg, which in turn is on a horizontal table. The coefficients of friction between the two blocks are µs = 0.300 and µk = 0.100. The coefficients of friction between the lower block and the rough table are µs = 0.500 and µk = 0.400. You apply a constant horizontal force to the lower block, just large enough to make this block start sliding out from between the upper block and the table.

Question

A block of mass m1 = 4.80 kg sits on top of a second block of mass m2 = 15.6 kg, which in turn is on a horizontal table. The coefficients of friction between the two blocks are µs = 0.300 and µk = 0.100. The coefficients of friction between the lower block and the rough table are µs = 0.500 and µk = 0.400. You apply a constant horizontal force to the lower block, just large enough to make this block start sliding out from between the upper block and the table.

Determine the magnitude force needed to initiate this motion.

Determine the acceleration you measure for each block in this situation

Answer 1

To determine the magnitude of the force needed to initiate the motion, we first need to calculate the maximum static friction between the blocks and the table.

The maximum static friction force (Fs) can be calculated using the formula:

Fs = µs * N

Where µs is the coefficient of static friction and N is the normal force.

The normal force (N) on the lower block can be calculated as the sum of the gravitational forces acting on both blocks. The normal force on the upper block is equal to its weight (m1 * g), and the normal force on the lower block is equal to the sum of its weight and the weight of the upper block (m1 * g + m2 * g).

So, the normal force (N) on the lower block is:

N = m1 * g + m2 * g

Substituting the values, where the mass of the first block (m1) is 4.80 kg, the mass of the second block (m2) is 15.6 kg, and the acceleration due to gravity (g) is 9.8 m/s^2:

N = (4.80 kg + 15.6 kg) * 9.8 m/s^2
N = 20.4 kg * 9.8 m/s^2
N = 200.16 N

Next, we can determine the maximum static friction force between the lower block and the table:

Fs = µs * N
Fs = 0.500 * 200.16 N
Fs = 100.08 N

Therefore, the magnitude of the force needed to initiate this motion is 100.08 N.

To determine the acceleration measured for each block, we can use Newton's Second Law, which states that the acceleration is equal to the net force acting on an object divided by its mass.

For the upper block, the net force is equal to the force of friction (which is equal to the maximum static friction force) acting in the opposite direction of motion. Therefore, the net force can be calculated as:

Fnet = -Fs

For the lower block, the net force is equal to the applied force acting in the positive direction of motion. So:

Fnet = F

Using the formula for acceleration (a = Fnet / m), we can calculate the accelerations for each block.

For the upper block:

a1 = -Fs / m1
a1 = -100.08 N / 4.80 kg
a1 = -20.85 m/s^2

For the lower block:

a2 = F / m2
a2 = 100.08 N / 15.6 kg
a2 = 6.42 m/s^2

Therefore, the acceleration measured for the upper block is -20.85 m/s^2 (negative because it is in the opposite direction of motion), and the acceleration measured for the lower block is 6.42 m/s^2.

Answer 2

First, find the force between the blocks.

m1*g*mu_s
That force will produce an accelearation on the upper block of a=F/m=g*mu_s
but to get that acceleartion, on has to apply a force to the lower block..
F=totalmass*a= (m1+m2)*g*mu_s
that answers the first question.

Now, the acceleration for each block
block 1: a=m1*g*mu<k>/m1
for block2: net force actin on lower block is pushing force- force on block1, or
(m1+m2)*g*mu_s - m1*g*mu_k
and acceleration of the lower block is that divided by m2.

check my thinking.