A 50KG BLOCK IS BEING PULLED BY
a 200-N FORCE ON A HORZONTAL ROUGH SURFACE AS SHOWN IN DIAGRAM.IF THE COEFFICIENT OF KINETIC FRICTION BETWEEN THE BLOCK AND THE SURFACE IS 0.3. FIND THE ACCELERATION OF THE BLOCK
To find the acceleration of the block, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's calculate the force of kinetic friction acting on the block. The force of kinetic friction can be determined using the equation:
\(f_k = \mu_k \times N\)
Where:
\(f_k\) is the force of kinetic friction
\(\mu_k\) is the coefficient of kinetic friction
\(N\) is the normal force
The normal force is equal to the weight of the block, which can be calculated using the equation:
\(N = mg\)
Where:
\(m\) is the mass of the block
\(g\) is the acceleration due to gravity (approximately 9.8 m/s²)
Therefore, \(N = 50 \, \text{kg} \times 9.8 \, \text{m/s²}\)
Now that we have calculated the normal force, we can find the force of kinetic friction using the coefficient of kinetic friction. Plugging in the values, we get:
\(f_k = 0.3 \times (50 \, \text{kg} \times 9.8 \, \text{m/s²})\)
Next, let's calculate the net force acting on the block. The net force is equal to the applied force minus the force of kinetic friction:
\(F_{net} = F_{\text{applied}} - f_k\)
Plugging in the values, we get:
\(F_{net} = 200 \, \text{N} - (0.3 \times (50 \, \text{kg} \times 9.8 \, \text{m/s²}))\)
Finally, we can find the acceleration of the block by dividing the net force by the mass of the block:
\(a = \frac{F_{net}}{m}\)
Plugging in the values, we get:
\(a = \frac{200 \, \text{N} - (0.3 \times (50 \, \text{kg} \times 9.8 \, \text{m/s²}))}{50 \, \text{kg}}\)
Simplifying the equation will give us the acceleration of the block.