A hockey puck is hit on a frozen lake and starts moving with a speed of 14.0 m/s. Five seconds later, its speed is 5.50 m/s.
(a) What is its average acceleration?
m/s2
(b) What is the average value of the coefficient of kinetic friction between puck and ice?
(c) How far does the puck travel during the 5.00 s interval?
m
for a) i got -1.70m/s^2
b) i need help
c) i got 48.8m
so can anyone help me with What is the average value of the coefficient of kinetic friction between puck and ice?
a. acceleration=deltaV/time=(5.5-14)/5
b. F=ma
mu*mg=ma
mu=a/g
c. how far?
d=vi*t+1/2 a t^2=14*5-1.7/2 * 25
To find the average value of the coefficient of kinetic friction between the puck and ice, we can use the formula for average acceleration:
Average acceleration = (final velocity - initial velocity) / (time taken)
(a) From the given information, the initial velocity of the puck is 14.0 m/s and the final velocity is 5.50 m/s. The time taken is 5.00 seconds.
Using the formula:
Average acceleration = (5.50 m/s - 14.0 m/s) / 5.00 s
Average acceleration = -8.50 m/s / 5.00 s
Average acceleration = -1.70 m/s^2
(b) To find the average value of the coefficient of kinetic friction, we can utilize the equation:
Average acceleration = coefficient of friction * acceleration due to gravity
Rearranging the equation to solve for the coefficient of friction:
Coefficient of friction = Average acceleration / acceleration due to gravity
The acceleration due to gravity is approximately 9.81 m/s^2.
Coefficient of friction = -1.70 m/s^2 / 9.81 m/s^2
Coefficient of friction ≈ -0.1737
Note: The negative sign indicates that the friction is acting in the opposite direction of motion.
(c) To determine how far the puck travels during the 5.00 s interval, we can use the formula:
Distance traveled = (initial velocity + final velocity) / 2 * time taken
Distance traveled = (14.0 m/s + 5.50 m/s) / 2 * 5.00 s
Distance traveled = 9.75 m/s * 5.00 s
Distance traveled = 48.8 m
Therefore, the average value of the coefficient of kinetic friction between the puck and ice is approximately -0.1737, and the puck travels a distance of 48.8 m during the 5.00 s interval.
To find the average value of the coefficient of kinetic friction between the puck and the ice, you can use the following steps:
Step 1: Calculate the acceleration of the puck.
The average acceleration of the puck can be calculated using the following formula:
Average Acceleration = (Final Velocity - Initial Velocity) / Time
In this case, the initial velocity is 14.0 m/s, the final velocity is 5.50 m/s, and the time is 5.0 seconds.
Average Acceleration = (5.50 m/s - 14.0 m/s) / 5.0 s
= -8.50 m/s / 5.0 s
= -1.70 m/s²
Therefore, the average acceleration of the puck is -1.70 m/s².
Step 2: Use the equation for acceleration due to friction.
The acceleration due to friction can be calculated using the following equation:
Frictional Force = Mass × Acceleration due to friction
Since the mass of the puck is not given in the question, we can cancel out the mass from both sides of the equation. This leaves us with the acceleration due to friction, which is equal to the average acceleration we calculated in Step 1.
Acceleration due to friction = -1.70 m/s²
Step 3: Calculate the total force of friction.
The total force of friction acting on the puck can be calculated using Newton's second law of motion:
Force of Friction = Mass × Acceleration
Since we canceled out the mass in Step 2, we can write the force of friction as:
Force of Friction = Mass × (-1.70 m/s²)
Step 4: Use the equation for the force of friction.
The force of friction can also be calculated using the equation:
Force of Friction = Coefficient of Friction × Normal Force
The normal force is the force exerted by a surface to support the weight of an object resting on it, and since the puck is on a horizontal surface, the normal force is equal to the weight of the puck.
However, since the weight of the puck is not given in the question, we need to use an alternate approach to find the coefficient of friction.
Step 5: Calculating the distance traveled by the puck.
Since the information about the distance traveled by the puck during the 5.00 seconds interval is given, we can use this information to find the coefficient of friction.
The distance traveled can be calculated using the formula:
Distance = Initial Velocity × Time + (1/2) × Average Acceleration × Time²
In this case, the initial velocity is 14.0 m/s, the time is 5.0 seconds, and the average acceleration is -1.70 m/s².
Distance = 14.0 m/s × 5.0 s + (1/2) × (-1.70 m/s²) × (5.0 s)²
= 70.0 m - 21.25 m
= 48.75 m
Therefore, the distance traveled by the puck during the 5.0 seconds interval is 48.75 meters.
Step 6: Calculate the coefficient of friction.
Now that we have the distance traveled by the puck, we can use it to find the coefficient of friction.
The equation for the force of friction can be rearranged as:
Force of Friction = Coefficient of Friction × Normal Force
Since the distance traveled is directly proportional to the force of friction, we can express the force of friction using the distance traveled, the average acceleration, and the mass of the puck (which we can substitute as normal force):
Force of Friction = Mass × Acceleration
Force of Friction = m × (-1.70 m/s²)
The distance traveled is equal to the force of friction acting on the puck, so we can replace the force of friction in the previous equation with the distance traveled:
Distance = m × (-1.70 m/s²)
48.75 m = m × (-1.70 m/s²)
Now we can solve for the mass (normal force):
Mass (normal force) = 48.75 m / (-1.70 m/s²)
Mass (normal force) = -28.68 kg·s²/m
Finally, substitute the mass (normal force) value into the equation for the force of friction and solve for the coefficient of friction:
Force of Friction = Coefficient of Friction × Normal Force
Force of Friction = Coefficient of Friction × (-28.68 kg·s²/m)
The force of friction is equal to the product of the coefficient of friction and the normal force, so we can substitute the force of friction with the mass (normal force) value:
(-28.68 kg·s²/m) = Coefficient of Friction × (-28.68 kg·s²/m)
This equation simplifies to:
Coefficient of Friction = 1
Therefore, the average value of the coefficient of kinetic friction between the puck and the ice is 1.