Due to a cart's sudden acceleration, a 200g wooden block remains on the front of the cart and does not slide or fall off. The mass of the cart is 10kg. The coefficient of static friction between the block and the front of the cart is 0.30.
Calculate the cart's minimum acceleration if the block is to remain in place.
To calculate the cart's minimum acceleration, we need to consider the forces acting on the wooden block.
First, let's determine the force of static friction between the block and the cart. The equation for static friction is given by:
Fs = μs * N
where Fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.
The normal force is equal to the weight of the block, which can be calculated as:
N = m * g
where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given that the mass of the block is 200g, which is 0.2 kg, we can calculate the weight:
N = 0.2 kg * 9.8 m/s^2
N = 1.96 N
Now we can calculate the force of static friction:
Fs = 0.30 * 1.96 N
Fs = 0.588 N
Since the block does not slide or fall off the cart, the force of static friction must equal the force pushing the block forward, which is equal to the mass of the cart multiplied by its acceleration:
Fs = F = m_cart * a
where m_cart is the mass of the cart and a is the acceleration.
Given that the mass of the cart is 10 kg, we can rearrange the equation to solve for the acceleration:
a = Fs / m_cart
a = 0.588 N / 10 kg
a = 0.0588 m/s^2
Therefore, the cart's minimum acceleration for the block to remain in place is 0.0588 m/s^2.