What force must be exerted on block A in order for block b not to fall. The coefficient of static friction between block A and B is 0.55, and the horizontal surface is frictionless.
A= 100kg and B=10kg
A is on the horizontal surface and B is attached to A.
To find the force required on block A in order for block B not to fall, we need to consider the forces acting on the system.
1. Weight of Block A (W_A): The weight of block A is given by the formula W_A = m_A * g, where m_A is the mass of block A (100 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²). Therefore, W_A = 100 kg * 9.8 m/s² = 980 N.
2. Weight of Block B (W_B): The weight of block B is given by the formula W_B = m_B * g, where m_B is the mass of block B (10 kg). Therefore, W_B = 10 kg * 9.8 m/s² = 98 N.
3. Frictional Force (F_friction): The maximum static frictional force can be calculated using the formula F_friction_max = μ_s * N, where μ_s is the coefficient of static friction (0.55) and N is the normal force. In this case, the normal force N is equal to the weight of block B (W_B). Therefore, F_friction_max = 0.55 * 98 N = 53.9 N.
4. Force Exerted on Block A (F_exerted): To prevent block B from falling, the force exerted on block A must be equal to or greater than the maximum static frictional force (F_friction_max). So, F_exerted ≥ F_friction_max.
In this scenario, since the coefficient of friction is greater than zero, block A requires a minimum force of 53.9 N (or approximately 54 N) to prevent block B from falling.
To determine the force required to prevent block B from falling, we need to consider the maximum force of static friction between block A and B. The maximum force of static friction is given by the equation:
F_friction = μ * N
where μ is the coefficient of static friction (given as 0.55) and N is the normal force acting on block B.
The normal force acting on block B is equal to its weight, since it is on a horizontal surface and there is no vertical acceleration. The weight of block B is given by:
W_B = m_B * g
where m_B is the mass of block B (given as 10 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the values into the equation, we have:
W_B = 10 kg * 9.8 m/s^2 = 98 N
Now we can calculate the maximum force of static friction:
F_friction = 0.55 * 98 N
F_friction = 53.9 N
Therefore, the force that must be exerted on block A in order for block B not to fall is approximately 53.9 N.