Question

a 200 kg crate is pushed horizontally with a force of 700 N. If the coefficient of friction is 0.2 calculate the acceleration of the crate

Answer 1

Answer:

$a=1.54\ m/s^2$

Explanation:

Net Force

The Second Newton's law states that an object acquires acceleration when an external unbalanced net force is applied to it.

That acceleration is proportional to the net force and inversely proportional to the mass of the object.

It can be expressed with the formula:

$\displaystyle a=\frac{F_n}{m}$

Where

Fn = Net force

m  = mass

The m=200 kg crate is pushed horizontally with a force Fa=700 N. The friction force opposes motion and a horizontal net force appears causing the acceleration.

The forces on the vertical direction are in balance since the crate does not accelerate in that direction, thus the weight and the normal force are equal:

N = W = mg

The friction force can be calculated by using the coefficient of friction μ:

$F_r=\mu N$

Calculating the normal force:

N = 200 * 9.8 = 1,960 N

The friction force is:

$F_r=0.2*1,960$

$F_r=392\ N$

The horizontal net force is:

$F_n = F_a-F_r=700\ N - 392\ N$

$F_n = 308\ N$

Finally, the acceleration is computed:

$\displaystyle a=\frac{308}{200}$

$\boxed{a=1.54\ m/s^2}$