Question - Calculating Acceleration With Friction
Solution:
The net force on the block is the difference between the applied force and the frictional force.Net force = Applied force - Frictional forceNet force = 25 N - 15 NNet force = 10 NTo find the acceleration (a), use Newton's second law, $$ F = ma $$, where F is the net force and m is the mass.Solving for acceleration $$ a $$,$$ a = \frac{F}{m} $$Substitute the known values into the equation,$$ a = \frac{10 \, \text{N}}{5 \, \text{kg}} $$The acceleration of the block is $$ 2 \, \text{m/s}^2 $$.
Tutor Solution:
To find the acceleration of the block, we will apply 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 ($$ F_{net} = m \cdot a $$).First, we need to determine the net force acting on the block. Since the block is on a horizontal surface, the net force will be the horizontal force applied to the block minus the frictional force opposing the motion.Given in the problem:- Applied force ($$F_{applied}$$) = 25 N- Frictional force ($$F_{friction}$$) = 15 N- Mass of the block ($$m$$) = 5 kgThe net force ($$F_{net}$$) is the difference between the applied force and the frictional force:\[ F_{net} = F_{applied} - F_{friction} \]\[ F_{net} = 25 \, N - 15 \, N \]\[ F_{net} = 10 \, N \]Now, we can use Newton's second law to find the acceleration ($$a$$):\[ F_{net} = m \cdot a \]\[ 10 \, N = 5 \, kg \cdot a \]Solving for acceleration $$a$$:\[ a = \frac{F_{net}}{m} \]\[ a = \frac{10 \, N}{5 \, kg} \]\[ a = 2 \, m/s^2 \]Thus, the acceleration of the block is $$2 \, m/s^2$$.
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