We can start by finding the maximum force of static friction, which is the force that keeps the box from sliding. The formula for the force of static friction is:
f_static = μ * N
where μ is the coefficient of static friction and N is the normal force, which in this case is equal to the gravitational force on the box (F_g = m_box * g). Thus,
f_static = μ * m_box * g
Plugging in the given values, we get:
f_static = 0.35 * 0.32 kg * 9.81 m/s^2 ≈ 1.10 N
Now, we can use Newton's second law (F = m*a) to find the minimum required acceleration for the cart to keep the box from falling. The only horizontal force acting on the box is the force of static friction, so we have:
F_static = m_box * a
Solving for a, we get:
a = F_static / m_box
Plugging in the calculated value of F_static, we get:
a = 1.10 N / 0.32 kg ≈ 3.44 m/s^2
Therefore, the minimum acceleration required to keep the box from falling is 3.44 m/s².
A 0.32 kg box of macaroni is held in place at the front of a 3.31 kg shopping cart only by the force of static friction as the shopping cart accelerates. Determine the minimum acceleration, in m/s 2, that the shopping cart must have if the box is to be kept from falling if the coefficient of static friction between the box and cart is 0.35.
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