A force F acts to the right on a 4.81 kg block.
A 2.53 kg block is stacked on top of the 4.81 kg
block and can slide on it with a coefficient of
friction of 0.2 between the blocks. The table
has a coefficient of friction of 0.23.
The acceleration of gravity is 9.8 m/s
2
.
The system is in equilibrium.
Find the force F required to accelerate the
4.81 kg block at 1.5 m/s
2
.
Answer in units of N
13
To find the force required to accelerate the 4.81 kg block at 1.5 m/s^2, we need to consider the forces acting on the system and use Newton's second law of motion.
Let's analyze the forces acting on the system:
1. Force F: This force acts to the right on the 4.81 kg block.
2. Weight of the 4.81 kg block: This force, W1, is equal to the mass (4.81 kg) multiplied by the acceleration due to gravity (9.8 m/s^2). W1 = 4.81 kg x 9.8 m/s^2.
3. Weight of the 2.53 kg block: This force, W2, is equal to the mass (2.53 kg) multiplied by the acceleration due to gravity (9.8 m/s^2). W2 = 2.53 kg x 9.8 m/s^2.
4. Friction force between the 4.81 kg block and the table: This force, Ff1, is equal to the coefficient of friction between the block and the table (0.23) multiplied by the normal force between them. The normal force, Fn1, is equal to the weight of the 4.81 kg block (W1).
5. Friction force between the 2.53 kg block and the 4.81 kg block: This force, Ff2, is equal to the coefficient of friction between the blocks (0.2) multiplied by the normal force between them. The normal force, Fn2, is equal to the weight of the 2.53 kg block (W2).
Now, let's write down the equations of motion using Newton's second law:
For the 4.81 kg block:
F - Ff1 - Ff2 = m1 * a
For the 2.53 kg block:
Ff2 - Fn2 = m2 * a
For the 4.81 kg block, we can substitute the values:
F - (0.23 * W1) - (0.2 * Fn2) = (4.81 kg) * (1.5 m/s^2)
For the 2.53 kg block:
0.2 * Fn2 - W2 = (2.53 kg) * (1.5 m/s^2)
Now, let's plug in the values and solve for F:
W1 = 4.81 kg * 9.8 m/s^2 = 47.138 N
W2 = 2.53 kg * 9.8 m/s^2 = 24.794 N
Substituting these values into the equations:
F - (0.23 * 47.138 N) - (0.2 * Fn2) = (4.81 kg) * (1.5 m/s^2)
0.2 * Fn2 - 24.794 N = (2.53 kg) * (1.5 m/s^2)
Solving these equations will give you the magnitude of force F required to accelerate the 4.81 kg block at 1.5 m/s^2.