A 100 N force is applied to the side of a crate resting on a level floor. The crate has a mass of 50 kg. If the coefficient of static friction is ìs = .25, is the 100 N force enough to make the crate accelerate? Explain why or why not.

no it doesnt

To determine if the 100 N force is enough to make the crate accelerate, we need to compare the force applied to the maximum static frictional force that can be exerted on the crate.

The formula for static frictional force is given by:

Fs = ìs * N

Where:
Fs = static frictional force
ìs = coefficient of static friction
N = normal force

The normal force (N) is the force exerted by the floor on the crate, which is equal to the weight of the crate.

Given that the mass of the crate is 50 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight of the crate as:

Weight = mass * acceleration due to gravity
= 50 kg * 9.8 m/s²
= 490 N

Now, we can calculate the maximum static frictional force:

Fs = ìs * N
= 0.25 * 490 N
= 122.5 N

Since the applied force of 100 N is less than the maximum static frictional force of 122.5 N, the force is not enough to make the crate accelerate. The static frictional force would counteract the applied force, preventing any acceleration.

To determine whether the 100 N force is enough to make the crate accelerate, we need to consider the forces acting on the crate and compare them.

1. Weight (W): The weight of an object is the force exerted on it due to gravity. It is calculated as the mass of the object multiplied by the acceleration due to gravity (9.8 m/s^2). In this case, the weight of the crate is calculated as W = m * g = 50 kg * 9.8 m/s^2 = 490 N.

2. Applied Force (F): The applied force is the force being exerted on the crate, in this case, 100 N.

3. Frictional Force (Ff): The frictional force opposes the motion between two surfaces in contact. In this scenario, the static frictional force is what we need to consider because the crate is at rest. The static frictional force (Ff) is calculated as Ff = ìs * N, where ìs is the coefficient of static friction and N is the normal force.

Now let's calculate the normal force (N):

The normal force (N) is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force equals the weight of the crate (490 N).

Now let's calculate the static frictional force (Ff) :

Ff = ìs * N = 0.25 * 490 N = 122.5 N

To determine if the crate will accelerate or not, we compare the applied force (F) to the static frictional force (Ff):

F (100 N) < Ff (122.5 N)

Since the applied force is less than the static frictional force, the crate will not start accelerating. The static frictional force will match and oppose the applied force, preventing the crate from moving.

In summary, the 100 N force is not enough to make the crate accelerate because the static frictional force is greater than the applied force.