Suppose you have a 114 kg wooden crate resting on a wood floor. Given that [tex]\mu_k = 0.3[/tex] and [tex]\mu_s = 0.5[/tex], what maximum force (in N) can you exert horizontally on the crate without moving it?

The maximum force of static friction (Fₛ) can be calculated using the formula: Fₛ = μₛ * N, where μₛ is the coefficient of static friction and N is the normal force. In this case, the normal force is equal to the weight of the crate, which is N = m * g, where m is the mass of the crate and g is the acceleration due to gravity.

1. Calculate the normal force (N):

N = 114 kg * 9.8 m/s² = 1117.2 N

2. Calculate the maximum static frictional force (Fₛ):

Fₛ = 0.5 * 1117.2 N = 558.6 N

3. The maximum horizontal force (F) that can be exerted without moving the crate is equal to the maximum static frictional force:

F = 558.6 N

So, the maximum force that can be exerted horizontally on the crate without moving it is 558.6 N.

To determine the maximum force that can be applied to a 114 kg wooden crate on a wooden floor without causing it to move, we need to consider the static friction between the crate and the floor. The maximum static frictional force can be calculated using the coefficient of static friction (μₛ) and the normal force (N).

First, we find the normal force, which is equal to the weight of the crate (mass multiplied by the acceleration due to gravity). In this case, the normal force is 1117.2 N. Next, we calculate the maximum static frictional force (Fₛ) by multiplying the coefficient of static friction (0.5) by the normal force, resulting in a value of 558.6 N.

Therefore, the maximum horizontal force (F) that can be exerted on the crate without moving it is 558.6 N. Exceeding this force would overcome the static friction, causing the crate to start moving.

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