a sled weighing 100 pounds reaches the foot of a hill with a speed of 40 feet/sec. The coefficient of kinetic friction between the sled and the horizon surface of the ice at the foot of the hill is 0.030. How far will the sled travel on the ice?
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To find out how far the sled will travel on the ice, we need to calculate the distance using the given information and applicable equations.
First, let's identify the relevant information given in the problem:
- Weight of the sled (W) = 100 pounds
- Speed of the sled (v) = 40 feet/sec
- Coefficient of kinetic friction (μ) = 0.030
The force of friction acting on the sled can be calculated using the equation:
Frictional Force (Ff) = μ * Normal Force
The normal force (N) can be calculated as:
Normal Force (N) = Weight (W)
Therefore, the frictional force acting on the sled can be calculated as:
Ff = μ * W
Now, let's calculate the frictional force:
Ff = 0.030 * 100 pounds
Next, we need to calculate the deceleration of the sled due to friction using Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
Since the mass is not given, we can use weight (W) to calculate mass using the equation:
Weight (W) = mass (m) * acceleration due to gravity (g)
Therefore, mass (m) can be calculated as:
m = W / g
Acceleration due to gravity (g) is approximately 32.2 feet/sec².
Now, we can calculate the deceleration:
F = m * a
Ff = m * a
Now, substitute the values:
0.030 * 100 pounds = m * a
Now, calculate the mass (m):
m = 100 pounds / 32.2 feet/sec²
Next, substitute the mass value and rearrange the equation to calculate the deceleration (a):
0.030 * 100 pounds = (100 pounds / 32.2 feet/sec²) * a
Solve for a:
a = (0.030 * 100 pounds * 32.2 feet/sec²) / 100 pounds
Now, we have the deceleration (a) of the sled. Since the sled is initially traveling at a constant speed, it will decelerate uniformly due to friction. Therefore, we can use the following equation to calculate the distance traveled (d) on the ice:
d = (v² / (2 * a))
Now, substitute the values:
d = (40 feet/sec)² / (2 * a)
Calculate the distance traveled:
d = (1600 feet²/sec²) / (2 * a)
Finally, substitute the value of a:
d = (1600 feet²/sec²) / (2 * ((0.030 * 100 pounds * 32.2 feet/sec²) / 100 pounds))
Now, solve for d to find the distance traveled by the sled on the ice.