On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 12.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is .10?
To find the distance the sled moves, we can use the equation for the work done by friction:
Work done by friction = Force of friction x Distance
The force of friction can be calculated using the formula:
Force of friction = coefficient of friction x Normal force
The normal force is equal to the weight of the sled, which can be calculated using the formula:
Weight = mass x acceleration due to gravity
Now, let's calculate the weight of the sled:
Weight = mass x acceleration due to gravity
Weight = 10.0 kg x 9.8 m/s^2
Weight = 98 N
Next, we can calculate the force of friction:
Force of friction = coefficient of friction x Normal force
Force of friction = 0.10 x 98 N
Force of friction = 9.8 N
Now, let's calculate the work done by friction:
Work done by friction = Force of friction x Distance
Since the sled starts from rest, all of the initial kinetic energy is converted into work done by friction:
Initial kinetic energy = 0.5 x mass x (initial velocity)^2
Initial kinetic energy = 0.5 x 10.0 kg x (12.2 m/s)^2
Initial kinetic energy = 0.5 x 10.0 kg x 148.84 m^2/s^2
Initial kinetic energy = 744.2 J
Work done by friction = Initial kinetic energy
Work done by friction = 744.2 J
Now, we can solve for the distance:
Work done by friction = Force of friction x Distance
Distance = Work done by friction / Force of friction
Distance = 744.2 J / 9.8 N
Distance ≈ 75.9 meters
Therefore, the sled moves approximately 75.9 meters on the frozen pond.
To find the distance the sled moves, we can use the equation of motion:
\[ \text{Distance} = \frac{{\text{Initial velocity}^2}}{{2 \times \text{Acceleration}}}\]
First, we need to find the acceleration of the sled. The only force acting on the sled once it starts moving is the force of friction, which can be calculated using the equation:
\[ \text{Friction force} = \text{Coefficient of friction} \times \text{Normal force}\]
The normal force is the force exerted by the surface perpendicular to the sled, which is equal to the weight of the sled \(mg\) (mass times gravity).
\[ \text{Normal force} = \text{mass} \times \text{gravity}\]
Once we have the friction force, we can use Newton's second law of motion to find the acceleration:
\[ \text{Friction force} = \text{mass} \times \text{acceleration}\]
Finally, we can substitute the values into the equation of motion to find the distance:
\[ \text{Distance} = \frac{{\text{Initial velocity}^2}}{{2 \times \text{acceleration}}}\]
Let's calculate the distance step by step:
Step 1: Calculate the normal force:
\[ \text{Normal force} = \text{mass} \times \text{gravity} = 10.0 \, \text{kg} \times 9.8 \, \text{m/s}^2\]
Step 2: Calculate the friction force:
\[ \text{Friction force} = \text{Coefficient of friction} \times \text{Normal force} = 0.10 \times (\text{mass} \times \text{gravity})\]
Step 3: Calculate the acceleration:
\[ \text{Friction force} = \text{mass} \times \text{acceleration} \implies \text{acceleration} = \frac{{\text{Friction force}}}{{\text{mass}}}\]
Step 4: Calculate the distance:
\[ \text{Distance} = \frac{{\text{Initial velocity}^2}}{{2 \times \text{acceleration}}}\]
Now you can substitute the values into the equations to find the distance.
It moves until the work done against friction,
M g * mu * X
equals the initial kinetic energy,
(1/2) M V^2
Mass M will cancel out. You don't need to know it