Two blocks with masses m1 = 20.7 kg and m2 = 55.5 kg, shown in the figure, are free to move. The coefficent of static friction between the blocks is 0.74 but the surface beneath m2 is frictionless.
What is the minimum force F required to hold m1 against m2?
Well, in order to determine the minimum force required to hold m1 against m2, let's use our amazing detective skills! We know that m2 is on a frictionless surface, so it won't exert any friction force on m1. The only force that acts between the two blocks is the force of static friction.
Now, the coefficient of static friction, given as 0.74, represents the maximum value of static friction. Since we want to find the minimum force, we can assume the static friction reaches its maximum and equals to the force required to hold m1 against m2.
Therefore, the minimum force F required to hold m1 against m2 would be equal to the maximum static friction force between the two blocks, which is determined by multiplying the coefficient of static friction by the normal force.
F = μ_s * N
Since we know the weights of the two blocks (m1 and m2), we can calculate their respective normal forces N1 and N2 using Newton's second law:
N1 = m1 * g
N2 = m2 * g
where g is the acceleration due to gravity. Then, substituting these values into our previous equation, we get:
F = 0.74 * N1
So, the minimum force F required to hold m1 against m2 is 0.74 times the weight of m1. Just make sure you don't clown around and exceed that force, or the blocks might start sliding like a circus act!
To determine the minimum force required to hold m1 against m2, we need to consider the forces acting on the system.
1. Start by analyzing the gravitational force acting on each block. The force of gravity on an object is given by the formula F = m * g, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
For m1:
F1_gravity = m1 * g
For m2:
F2_gravity = m2 * g
2. Next, consider the frictional force between the two blocks. Since the coefficient of static friction between the blocks is given, we can calculate the maximum frictional force between them using the formula F_friction = μ * N, where μ is the coefficient of static friction and N is the normal force.
The normal force in this case is the vertical force exerted by m2 on m1, which is equal in magnitude to m1 * g according to Newton's third law.
F_friction = μ * N
= μ * (m1 * g)
3. Now, we need to determine the minimum force required to hold m1 against m2. Since m2 is frictionless, the only force that can prevent m1 from sliding is the frictional force between m1 and m2.
The minimum force required is equal to the maximum frictional force:
F_minimum = F_friction
= μ * (m1 * g)
To calculate the answer, substitute the values of the coefficients and masses into the equation F_minimum = μ * (m1 * g).