A block moving to the right at 12
m/s is placed on a surface having a
friction coefficient of 0.3. Find the time
in seconds it takes for the block to stop.
To find the time it takes for the block to stop, we need to determine the deceleration of the block due to friction and then use the equation of motion.
The deceleration caused by friction can be calculated using the formula:
a = μ * g
where "a" is the acceleration due to friction, "μ" is the friction coefficient, and "g" is the acceleration due to gravity (approximately 9.8 m/s²).
In this case, the friction coefficient is given as 0.3. So the acceleration due to friction is:
a = 0.3 * 9.8 m/s² = 2.94 m/s² (rounded to two decimal places)
Since the block is moving to the right, the deceleration will act in the opposite direction, or to the left. The negative sign accounts for this inverse direction.
Now, we can use the equation of motion to calculate the time it takes for the block to stop:
v = u + at
where "v" is the final velocity (which is 0 m/s when the block stops), "u" is the initial velocity (12 m/s to the right), "a" is the deceleration due to friction (2.94 m/s² to the left), and "t" is the time we want to find.
Substituting the values into the equation, we can solve for "t":
0 = 12 m/s + (-2.94 m/s²) * t
Rearranging the equation:
2.94 m/s² * t = 12 m/s
Dividing both sides by 2.94 m/s²:
t = 12 m/s / 2.94 m/s² ≈ 4.08 seconds (rounded to two decimal places)
Therefore, it takes approximately 4.08 seconds for the block to stop.