A block of wood of mass 6.0 kg slides along a skating rink at 12.5 m/s^2 [w] . The block slides onto a rough section of ice that exerts a force of 30 N force of friction on the block of wood. The acceleration of the block of wood is 5.0 m/s^2 [E] and it takes 2.5s to stop. How far does the block slide after friction begins to act on it ?
16.0m
To determine the distance the block slides after friction begins to act on it, we need to find the distance traveled during the time interval of 2.5 seconds.
Given:
Mass of the block (m) = 6.0 kg
Acceleration of the block, initial (a1) = 12.5 m/s^2 [w]
Acceleration of the block, final (a2) = 5.0 m/s^2 [E]
Force of friction (F) = 30 N
Time interval (t) = 2.5 s
First, let's calculate the net force acting on the block.
Net force (Fnet) = Mass x Acceleration
Fnet = 6.0 kg x 12.5 m/s^2 [w]
Fnet = 75 N [w]
Since the friction force opposes the motion of the block, it acts in the opposite direction to the net force. Therefore, the friction force can be written as:
Force of friction (F) = - Fnet
30 N = -75 N
Next, let's calculate the deceleration of the block.
Force of friction (F) = Mass x Deceleration
30 N = 6.0 kg x Deceleration
Deceleration = 30 N / 6.0 kg
Deceleration = 5.0 m/s^2 [W]
Now, we can calculate the initial velocity of the block.
a2 = (vf - vi) / t
5.0 m/s^2 [E] = (0 m/s - vi) / 2.5 s
-12.5 m/s = -vi
vi = 12.5 m/s [w]
Using the formula for average velocity:
Average velocity (v_avg) = (vi + vf) / 2
v_avg = (12.5 m/s + 0 m/s) / 2
v_avg = 6.25 m/s
Finally, we can calculate the distance traveled using the formula:
Distance = Average Velocity x Time
Distance = 6.25 m/s x 2.5 s
Distance = 15.625 m
Therefore, the block slides a distance of 15.625 meters after friction begins to act on it.
To determine the distance the block slides after friction begins to act on it, we need to calculate the time it takes for the block to stop.
Given:
- Mass of the block (m): 6.0 kg
- Initial acceleration (a): 12.5 m/s^2 to the west (opposite to motion)
- Friction force (Ff): 30 N to the east (opposite to motion)
- Final acceleration (af): 5.0 m/s^2 to the east (opposite to motion)
- Time (t): 2.5 s
First, we need to determine the net force acting on the block after friction begins. To do this, we subtract the friction force from the force that was initially accelerating the block.
Net force (Fnet) = Force accelerating the block (Fa) - Friction force (Ff)
The force accelerating the block can be calculated using Newton's second law:
Fa = mass (m) × acceleration (a)
Substituting the given values:
Fa = 6.0 kg × 12.5 m/s^2 = 75 N
Now we can calculate the net force:
Fnet = Fa - Ff = 75 N - 30 N = 45 N
The net force acting on the block is 45 N to the west.
Next, we can use the second law of motion to find the time it takes for the block to stop:
Fnet = mass (m) × acceleration (af)
Rearranging the formula:
t = (mass (m) × acceleration (af)) / Fnet
Substituting the given values:
t = (6.0 kg × 5.0 m/s^2) / 45 N = 0.67 s
Therefore, it takes approximately 0.67 seconds for the block to stop.
To determine the distance the block slides after friction begins, we can use the equation:
Distance (d) = Initial velocity (vi) × time (t) + (1/2) × acceleration (af) × (time (t))^2
Since the block initially slides at a constant velocity, the initial velocity (vi) is equal to the constant velocity and can be calculated using the initial acceleration (a) and time (t) before friction begins to act:
vi = a × t = 12.5 m/s^2 × 2.5 s = 31.25 m/s
Now, we can calculate the distance:
d = vi × t + (1/2) × af × (t)^2
= 31.25 m/s × 2.5 s + (1/2) × 5.0 m/s^2 × (2.5 s)^2
= 78.125 m + 1.25 m = 79.375 m
Therefore, the block slides approximately 79.375 meters after friction begins to act on it.