To determine how fast the man can accelerate the blocks without the smaller block sliding off the top, we need to consider the maximum static friction between the two blocks.
The maximum static friction force (F_friction) between two surfaces can be calculated using the equation:
F_friction = μ_s * F_normal
Where:
- μ_s is the coefficient of static friction
- F_normal is the normal force between the two surfaces
First, we need to calculate the normal force (F_normal) acting on the smaller block. The normal force is equal to the weight (mg) of the block, where m is the mass and g is the acceleration due to gravity (9.8 m/s^2).
For the smaller block:
m_smaller = 15 kg
F_normal_smaller = m_smaller * g = 15 kg * 9.8 m/s^2 = 147 N
Next, we can calculate the maximum static friction force (F_friction) between the two blocks using the coefficient of static friction (μ_s). In this case, it's 0.45.
F_friction = μ_s * F_normal_smaller = 0.45 * 147 N = 66.15 N
The maximum static friction force (F_friction) is also equal to the force the man exerts on the larger block (F_man) to accelerate the blocks.
Finally, we can calculate the maximum acceleration (a) the man can achieve without having the smaller block slide off the top using Newton's second law of motion:
F_man = (mass_of_larger_block + mass_of_smaller_block) * a
Rearranging the equation and substituting the values:
66.15 N = (25 kg + 15 kg) * a
66.15 N = 40 kg * a
a = 66.15 N / 40 kg ≈ 1.65 m/s^2
Therefore, the man can accelerate the blocks at a maximum rate of approximately 1.65 m/s^2 without having the smaller block slide off the top.
A man stacks a small block of wood on top of a larger block and then moves both by pushing the
bottom block. The large block has a mass of 25 kg, and the smaller block has a mass of 15 kg. Thecoefficient of static friction between the two blocks is 0.45. How fast can the man accelerate the blocks without having the smaller block slide off the top?
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