You push a 45 kg wooden box across a wooden floor at a constant speed of 1.0 m/s. The coefficient of kinetic friction is 0.15. Now you double the force on the box. How long would it take for the velocity of the crate to double to 2.0 m/s?

To find out how long it would take for the velocity of the crate to double to 2.0 m/s, we can use the equation:

F_net = m * a

where,
F_net is the net force acting on the crate,
m is the mass of the crate,
and a is the acceleration of the crate.

When pushing the crate at a constant speed, the net force is equal to the force of kinetic friction, which can be calculated using the equation:

f_kinetic = μ * F_normal

where,
f_kinetic is the force of kinetic friction,
μ is the coefficient of kinetic friction,
and F_normal is the normal force acting on the crate.

In this case, the normal force is equal to the weight of the crate, which can be calculated using the equation:

F_normal = m * g

where,
g is the acceleration due to gravity (approximately 9.8 m/s^2).

Let's calculate the force of kinetic friction and the normal force first:

F_normal = m * g
F_normal = 45 kg * 9.8 m/s^2
F_normal = 441 N

f_kinetic = μ * F_normal
f_kinetic = 0.15 * 441 N
f_kinetic = 66.15 N

Since the net force is equal to the force of kinetic friction, the acceleration of the crate is zero:

F_net = f_kinetic
m * a = 66.15 N
45 kg * a = 66.15 N
a ≈ 1.469 m/s^2

Now, let's find out the how long it would take for the velocity to double to 2.0 m/s using the equation:

v = u + a * t

where,
v is the final velocity,
u is the initial velocity,
a is the acceleration,
and t is the time taken.

Since the initial velocity is 1.0 m/s, and the final velocity is 2.0 m/s, we can rearrange the equation:

t = (v - u) / a
t = (2.0 m/s - 1.0 m/s) / 1.469 m/s^2
t ≈ 0.681 seconds

Therefore, it would take approximately 0.681 seconds for the velocity of the crate to double to 2.0 m/s when the force is doubled.

To answer this question, we can use the concept of Newton's second law of motion and the equation for force of friction. Let's break it down step by step:

1. Calculate the force of friction acting on the box:
The force of friction can be calculated using the equation:
Force of friction = coefficient of friction * normal force
The normal force can be determined by multiplying the mass of the box by the acceleration due to gravity (9.8 m/s^2):
Normal force = mass * gravity
Thus, the force of friction acting on the box is given by:
Force of friction = coefficient of friction * mass * gravity

2. Calculate the initial force required to push the box at a constant speed of 1.0 m/s:
Since the box is moving at a constant speed, the force applied to move the box must be equal to the force of friction. Mathematically, this can be written as:
Force applied = Force of friction

3. Double the force applied:
The question asks for the time it would take for the velocity of the crate to double to 2.0 m/s. Therefore, we need to determine how long it would take for the force applied (or the net force) to increase by a factor of 2 (or double).

4. Calculate the new force required to double the velocity:
Since the force applied is directly proportional to the net force, doubling the force applied will result in a doubled net force. Therefore, the new net force can be calculated as:
New force applied = 2 * Force applied

5. Calculate the acceleration of the crate using the new force:
Using Newton's second law of motion, we know that the net force applied to an object is equal to the mass of the object multiplied by its acceleration. Mathematically, this can be written as:
New force applied = mass * acceleration
Rearranging this equation, we can solve for acceleration:
acceleration = New force applied / mass

6. Calculate the time it takes for the velocity to double:
To find the time it takes for the velocity of the crate to double, we need to determine the rate of change of its velocity, which is given by the acceleration. Mathematically, this can be written as:
acceleration = change in velocity / time
Rearranging this equation, we can solve for time:
time = change in velocity / acceleration

By following these steps and plugging in the given values, you can calculate the time it would take for the velocity of the crate to double to 2.0 m/s.

When the applied force doubles, the friction force will remain the same but the net force will go from zero to a new value equal to the friction force, M*g*Uk.

The acceleration rate will be
a = Fnet/m = m g *Uk /m = g Uk

Require that a*T = delta V = 1.0 m/s, and solve for T