on a frozen pond , a 12 kg sled is given a kick that imparts to it an initial speed of 7.7 m/s. the coefficient of kinetic friction between sled and ice is 0.1. find the distance of the sled moves before coming to rest . the acceleration of gravity is 9.8m/s . answer in units is m l
To find the distance the sled moves before coming to rest, we first need to calculate the deceleration force acting on the sled due to the kinetic friction.
Step 1: Calculate the force of friction
The formula for the force of kinetic friction is given by:
F_friction = μ * N
where
μ is the coefficient of kinetic friction (0.1 in this case)
N is the normal force acting on the sled
Step 2: Calculate the normal force
Since the sled is on a horizontal surface, the weight of the sled will act as the normal force.
N = m * g
where
m is the mass of the sled (12 kg)
g is the acceleration due to gravity (9.8 m/s^2)
Step 3: Calculate the force of friction
F_friction = μ * N
Step 4: Calculate the deceleration
Using Newton's second law, we can find the deceleration force acting on the sled:
F_net = m * a
a = F_net / m
where
F_net is the net force acting on the sled (in this case, the force of friction acting in the opposite direction of motion)
Step 5: Calculate the distance using the kinematic equation
We can use the kinematic equation to find the distance the sled moves:
v^2 = v_0^2 + 2 * a * d
where
v is the final velocity (0 m/s, since the sled comes to rest)
v_0 is the initial velocity (7.7 m/s)
a is the deceleration force calculated in step 4
d is the distance traveled by the sled
Now let's calculate the distance:
Step 1: Calculate the force of friction
F_friction = 0.1 * (12 kg * 9.8 m/s^2) #=> F_friction = 11.76 N
Step 2: Calculate the normal force
N = 12 kg * 9.8 m/s^2 #=> N = 117.6 N
Step 3: Calculate the force of friction
F_friction = 0.1 * 117.6 N #=> F_friction = 11.76 N
Step 4: Calculate the deceleration
a = -F_friction / m #=> a = -11.76 N / 12 kg (the negative sign indicates deceleration)
Step 5: Calculate the distance
0^2 = (7.7 m/s)^2 + 2 * a * d
0 = 59.29 m^2/s^2 + 2 * (-11.76 m/s^2) * d
0 = 59.29 m^2/s^2 - 23.52 m^2/s^2 * d
23.52 m^2/s^2 * d = 59.29 m^2/s^2
d = 59.29 m^2/s^2 / 23.52 m^2/s^2
d = 2.52 m
Therefore, the sled moves approximately 2.52 meters before coming to rest.
To find the distance the sled moves before coming to rest, we need to determine the deceleration of the sled due to friction.
Here are the steps to solve the problem:
1. Calculate the force of kinetic friction acting on the sled:
The force of kinetic friction can be calculated using the formula:
Friction force = coefficient of kinetic friction * normal force
The normal force is the force equal to the weight of the sled, which can be calculated as:
Normal force = mass of the sled * acceleration due to gravity
Substituting the given values into the formula:
Normal force = 12 kg * 9.8 m/s^2
Friction force = 0.1 * (12 kg * 9.8 m/s^2)
2. Calculate the deceleration of the sled due to friction:
The deceleration can be calculated using the formula:
Deceleration = Friction force / mass of the sled
Substituting the values:
Deceleration = Friction force / 12 kg
3. Calculate the time it takes for the sled to come to rest:
The initial velocity of the sled is 7.7 m/s. The final velocity when the sled comes to rest is 0 m/s. As we know the acceleration due to friction acting on the sled, we can use the following formula to find the time it takes to come to rest:
Final velocity = Initial velocity + (acceleration * time)
Rearranging the formula:
Time = (Final velocity - Initial velocity) / acceleration
4. Calculate the distance the sled moves before coming to rest:
The distance can be calculated using the formula:
Distance = Initial velocity * time + (1/2) * acceleration * time^2
By following these steps and substituting the values given in the question, you can find the distance the sled moves before coming to rest in meters.
the initial energy of the sled is ... 1/2 * 12 * 7.7^2
this energy is dissipated by work against friction over the distance
... d * 12 * 9.8 * 0.1
1/2 * 12 * 7.7^2 = d * 12 * 9.8 * 0.1