A force is applied to a 22.5 kg object causing it to move at a constant velocity of 4.2 m/s with a coefficient of friction of 0.44. Suddenly, the applied force is removed, causing friction to be the only force acting on the object. How long will it take the object to come to rest.

See previous post: yesterday, 9:38PM.

To determine how long it will take for the object to come to rest, we need to calculate the deceleration caused by friction.

First, let's find the force of friction using the formula:

Force of friction = coefficient of friction * normal force

The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, since the object is on a horizontal surface, the normal force is equal to the weight of the object, which can be calculated as:

Weight = mass * acceleration due to gravity

The acceleration due to gravity is approximately 9.8 m/s^2.

Weight = 22.5 kg * 9.8 m/s^2 = 220.5 N

Now we can find the force of friction:

Force of friction = 0.44 * 220.5 N = 97.02 N

The force of friction acts in the opposite direction to the motion of the object, so it will cause the object to decelerate.

Next, we can use Newton's second law of motion to calculate the deceleration:

Force = mass * acceleration

In this case, the force is the force of friction, and the mass is 22.5 kg.

97.02 N = 22.5 kg * acceleration

Solving for acceleration, we get:

acceleration = 97.02 N / 22.5 kg = 4.32 m/s^2

Since the object is initially moving at 4.2 m/s and it is decelerating at a rate of 4.32 m/s^2, we can use the equation:

Final velocity^2 = Initial velocity^2 + 2 * acceleration * distance

We want to find the distance traveled before the object comes to rest, so we set the final velocity to zero:

0 = (4.2 m/s)^2 + 2 * (-4.32 m/s^2) * distance

Solving for distance, we get:

distance = (4.2 m/s)^2 / (2 * 4.32 m/s^2) = 4.1 m

Finally, we can use the equation:

time = distance / velocity

time = 4.1 m / 4.2 m/s ≈ 0.98 s

Therefore, it will take approximately 0.98 seconds for the object to come to rest.