A block M1 of mass 20.0 kg sits on top of a larger block M2 of mass 30.0 kg which sits on a flat surface. The kinetic friction coefficient between the upper and lower block is 0.415. The kinetic friction coefficient between the lower block and the flat surface is 0.115. A horizontal force F = 97 N pushes against the upper block, causing it to slide. The friction force between the blocks then causes the lower block to slide also. Find the magnitude of the acceleration of the upper block.
b)Find the magnitude of the acceleration of the lower block.
I have no idea how to do this problem. Can someone please help and show how you did it? Thank you.
To solve this problem, we need to apply Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration (F = ma).
Let's break down the problem step by step:
1. Find the net force acting on the upper block:
- The horizontal force pushing against the upper block is F = 97 N.
- The friction force between the upper and lower block opposes the motion and can be calculated using the formula: F_friction = μ_k * N, where μ_k is the coefficient of friction and N is the normal force.
- The normal force on the upper block is equal to its weight, which is given by N = m1 * g, where m1 is the mass of the upper block (20.0 kg) and g is the acceleration due to gravity (9.8 m/s^2).
- Substituting the values, we get F_friction1 = 0.415 * 20.0 kg * 9.8 m/s^2 = 81.17 N.
- Since the friction force opposes the applied force, the net force on the upper block is F_net1 = F - F_friction1 = 97 N - 81.17 N = 15.83 N.
2. Calculate the acceleration of the upper block:
- Using Newton's second law, we have F_net1 = m1 * a1, where m1 is the mass of the upper block (20.0 kg) and a1 is the acceleration of the upper block.
- Rearranging the equation, we get a1 = F_net1 / m1 = 15.83 N / 20.0 kg = 0.792 m/s^2.
3. Find the net force acting on the lower block:
- The friction force between the lower block and the flat surface can be calculated using the formula: F_friction2 = μ_k * N, where μ_k is the coefficient of friction and N is the normal force.
- The normal force on the lower block is equal to its weight plus the weight of the upper block, which is given by N = (m1 + m2) * g, where m1 is the mass of the upper block (20.0 kg), m2 is the mass of the lower block (30.0 kg), and g is the acceleration due to gravity (9.8 m/s^2).
- Substituting the values, we get F_friction2 = 0.115 * (20.0 kg + 30.0 kg) * 9.8 m/s^2 = 64.07 N.
- The friction force between the upper and lower block now acts as an external force on the lower block, so the net force on the lower block is F_net2 = F_friction1 - F_friction2 = 81.17 N - 64.07 N = 17.10 N.
4. Calculate the acceleration of the lower block:
- Using Newton's second law, we have F_net2 = m2 * a2, where m2 is the mass of the lower block (30.0 kg) and a2 is the acceleration of the lower block.
- Rearranging the equation, we get a2 = F_net2 / m2 = 17.10 N / 30.0 kg = 0.570 m/s^2.
Therefore, the magnitude of the acceleration of the upper block is 0.792 m/s^2, and the magnitude of the acceleration of the lower block is 0.570 m/s^2.