A child on a sled reaches the bottom of a hill with a velocity of 12.0 m/s and travels 22.0 m along a horizontal straightaway to a stop.
If the child and sled together have a mass of 59.0 kg, what is the magnitude of the average retarding force on the sled on the horizontal straightaway?
To find the magnitude of the average retarding force on the sled, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's find the acceleration of the sled. We can use the equation of motion v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.
Given:
Final velocity, v = 0 m/s (since the sled comes to a stop)
Initial velocity, u = 12.0 m/s
Distance, s = 22.0 m
v² = u² + 2as
0² = (12.0 m/s)² + 2a(22.0 m)
Simplifying the equation:
0 = 144.0 m²/s² + 44.0 m²/s² * a
Rearranging and solving for acceleration:
a = -144.0 m²/s² / (44.0 m²/s²)
a = -3.27 m/s²
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, representing the deceleration of the sled.
Next, we can calculate the magnitude of the average retarding force using Newton's second law of motion:
F = m * a
F = 59.0 kg * (-3.27 m/s²)
F = -192.93 N
The magnitude of the average retarding force on the sled on the horizontal straightaway is approximately 192.93 N.
To find the magnitude of the average retarding force on the sled, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, we need to find the acceleration first.
We can use the equation of motion: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
Given:
- Initial velocity (u) = 12.0 m/s
- Final velocity (v) = 0 m/s (the sled comes to a stop)
- Displacement (s) = 22.0 m
Rearranging the equation, we get:
a = (v^2 - u^2) / (2s)
Substituting the values, we have:
a = (0^2 - 12.0^2) / (2 * 22.0)
Simplifying this equation, we get:
a = (-144) / (44)
a ≈ -3.27 m/s^2 (negative sign indicates deceleration or retardation)
Now we can use Newton's second law to find the force:
F = m * a
Given:
- Mass (m) = 59.0 kg
- Acceleration (a) = -3.27 m/s^2
Substituting the values, we have:
F = 59.0 kg * (-3.27 m/s^2)
Simplifying this equation, we get:
F ≈ -192.93 N
The magnitude of the average retarding force on the sled on the horizontal straightaway is approximately 192.93 N.