What is the acceleration of the upper block? The coefficient of kinetic friction between the lower block and upper block is 0.0005. The coefficient of kinetic friction between lower block and floor is 0.0001. Upper block is 1kg, lower block is 2kg, and Force of 20N is applied to lower block.
Here's a picture:
img217.imageshack.us/img217/3526/2505100050.jpg
I got 20 m/s as the acceleration of the upper block. Is this right?
Sorry here's the picture:
img245.imageshack.us/img245/3526/2505100050.jpg
No; it's not right. First of all, 20 m/s is a speed, not an acceleration.
The two masses accelerate at different rates because there is very little friction and the top mass tends to be left behind. The top mass (#2) is accelerated only by the kinetic friction force between the blocks, which is
0.0005 M2 g = M2*a2, so
a2 = 0.0005 g = .0049 m/s^2
and the force that accelerates M2 is just M2 a2 = 0.0049 N
The force that accelerates M1 is
20N - (3 kg)(0.0001)g - 0.0049 = M1*a1
20N - .0029N - .0049N = 2 a1
a1 = 9.996 m/s^2
Thank you! I see where I went wrong
To find the acceleration of the upper block, we need to first calculate the net force acting on it.
First, let's analyze the forces acting on the lower block:
1. The applied force: It is given as 20N.
2. The force of kinetic friction between the lower block and the upper block: This force acts opposite to the direction of motion, and its magnitude can be calculated using the equation:
F_friction = μ_k * N
where μ_k is the coefficient of kinetic friction (0.0005) and N is the normal force.
The normal force is the force exerted by the lower block on the upper block, which is equal to its weight (mg). So,
F_friction = μ_k * mg
3. The force of kinetic friction between the lower block and the floor: This force also acts opposite to the direction of motion, and its magnitude can be calculated using the same equation:
F_friction_floor = μ_k * N_floor
where μ_k is the coefficient of kinetic friction between the lower block and the floor (0.0001) and N_floor is the normal force exerted by the floor on the lower block.
The normal force exerted by the floor on the lower block can be calculated using the equation:
N_floor = m_lower * g
Now, let's proceed with the calculations:
1. Calculate the force of kinetic friction between the lower and upper blocks:
F_friction = μ_k * m_upper * g
2. Calculate the force of kinetic friction between the lower block and the floor:
F_friction_floor = μ_k * m_lower * g
3. Calculate the net force acting on the lower block:
net_force = applied_force - F_friction - F_friction_floor
net_force = 20N - F_friction - F_friction_floor
4. Use Newton's second law of motion (F = ma) to find the acceleration of the lower block:
net_force = m_lower * a_lower
5. Since the acceleration of the lower block is the same as the acceleration of the upper block (due to their mechanical connection), the acceleration of the upper block is also a_lower.
Now, let's substitute the given values into the equations:
m_upper = 1kg
m_lower = 2kg
μ_k = 0.0005
μ_floor = 0.0001
applied_force = 20N
1. Calculate the force of kinetic friction between the lower and upper blocks:
F_friction = μ_k * m_upper * g
F_friction = 0.0005 * 1kg * 9.8 m/s^2
F_friction = 0.0049 N
2. Calculate the force of kinetic friction between the lower block and the floor:
F_friction_floor = μ_floor * m_lower * g
F_friction_floor = 0.0001 * 2kg * 9.8 m/s^2
F_friction_floor = 0.00196 N
3. Calculate the net force acting on the lower block:
net_force = applied_force - F_friction - F_friction_floor
net_force = 20N - 0.0049 N - 0.00196 N
net_force = 19.99314 N
4. Use Newton's second law of motion (F = ma) to find the acceleration of the lower block:
net_force = m_lower * a_lower
19.99314 N = 2kg * a_lower
a_lower = 9.99657 m/s^2
5. Since the acceleration of the lower block is the same as the acceleration of the upper block, the acceleration of the upper block is also:
a_upper = 9.99657 m/s^2
So, the correct acceleration of the upper block is approximately 9.997 m/s^2, not 20 m/s.