8. The coefficient of static friction between a 150-kg box of medical equipment and the floor is 0.35. Would 450-N force applied horizontally be enough to cause the box to move from rest?

see your later post.

To determine if a 450-N force applied horizontally would be enough to cause the box to move from rest, we need to compare it to the maximum force of static friction.

The formula for static friction is:

Fs ≤ μs * N

Where:
Fs = Force of static friction
μs = Coefficient of static friction
N = Normal force

The normal force (N) is equal to the weight of the box, which can be calculated by multiplying the mass (m) by the acceleration due to gravity (g):

N = m * g

Given:
Mass of the box (m) = 150 kg
Coefficient of static friction (μs) = 0.35
Acceleration due to gravity (g) = 9.8 m/s^2

First, let's calculate the normal force:

N = 150 kg * 9.8 m/s^2
N = 1470 N

Now, we can calculate the maximum force of static friction:

Fs ≤ 0.35 * 1470 N
Fs ≤ 514.5 N

The maximum force of static friction is 514.5 N.

Since the applied force of 450 N is less than the maximum static friction force, the box would not move from rest with this force alone.

To determine whether the applied force of 450 N is enough to cause the box to move from rest, we can use the concept of static friction.

Static friction is the force that opposes the motion of an object at rest. It depends on two factors: the coefficient of static friction and the normal force acting on the object.

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,
N is the normal force.

The normal force is equal to the weight of the object, which is given by:

N = m * g

Where:
m is the mass of the object, which is 150 kg in this case,
g is the acceleration due to gravity, which is approximately 9.8 m/s².

Substituting the values into the equation:

N = 150 kg * 9.8 m/s² = 1470 N

Now, using the given coefficient of static friction, which is 0.35, we can calculate the force of static friction:

Fs = 0.35 * 1470 N = 514.5 N

Since the applied force of 450 N is smaller than the force of static friction (514.5 N), the box will not move from rest. Therefore, the 450-N force is not enough to cause the box to move.