A 156 g hockey puck is initially travelling with a speed of 18 m/s. The force of friction acting on the puck is 0.30 N. If no other forces act on the hockey puck, how far will it slide before coming to rest? (4T, 1C)
F=m a
-0.30 = 0.156 a
a = - 1.92 m/s^2
v= Vi + a t
0 = 18 - 1.92 t
t = 9.38 seconds
x = Xi + Vi t + (1/2) a t^2
x = 0 + 18 (9.38) - 0.96 (9.38)^2
= 169 - 84.5
= 84.5 meters
v^2 = 2as = 2(F/m)s
s = mv^2/(2F)
now plug in your numbers
Why did the hockey puck go to the circus? Because it wanted to slide and do tricks! But don't worry, I'll calculate how far it will slide before coming to rest. We can use the equation:
Force of friction = mass × acceleration
The force of friction is given as 0.30 N, and we need to find the acceleration. We know that the final velocity is 0 m/s because the puck comes to rest. The initial velocity is 18 m/s, and the mass of the puck is 156 g, or 0.156 kg.
Using the equation:
0.30 N = 0.156 kg × a
We can solve for acceleration:
a = 0.30 N / 0.156 kg ≈ 1.92 m/s²
Now, we can use the kinematic equation:
v² = u² + 2as
Where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.
Plugging in the values:
0 = (18 m/s)² + 2(1.92 m/s²) × s
solving for s:
s ≈ - (18 m/s)² / (2 × 1.92 m/s²)
s ≈ -163.13 m²/s² / 3.84 m/s²
s ≈ -42.46 m
Since distance cannot be negative, let's consider the absolute value:
s ≈ 42.46 m
So, the hockey puck will slide approximately 42.46 meters before coming to rest. Keep an eye out for any slapstick comedy along the way!
To find the distance the hockey puck will slide before coming to rest, we can use the equation:
\[v^2 = u^2 + 2as\]
Where:
- \(v\) is the final velocity (which is 0 m/s since the puck comes to rest)
- \(u\) is the initial velocity (18 m/s)
- \(a\) is the acceleration (which is caused by the friction force)
- \(s\) is the distance traveled
We know that the acceleration is caused by the friction force:
\[F_{\text{friction}} = \mu{N}\]
Where:
- \(F_{\text{friction}}\) is the friction force (0.30 N)
- \(\mu\) is the coefficient of friction
- \(N\) is the normal force
Since there are no other forces acting on the puck, the normal force is equal to the weight of the puck:
\[N = mg\]
Where:
- \(m\) is the mass of the puck (156 g = 0.156 kg)
- \(g\) is the acceleration due to gravity (9.8 m/s²)
So, we can substitute \(N\) in the friction equation:
\[F_{\text{friction}} = \mu{mg}\]
Solving for \(\mu\):
\[\mu = \frac{F_{\text{friction}}}{mg}\]
Now we can substitute the known values into the equation for acceleration:
\[0 = u^2 + 2as\]
\[0 = (18 \, \text{m/s})^2 + 2 \left(\frac{F_{\text{friction}}}{m}\right) s\]
Simplifying:
\[0 = 324 + 2 \left(\frac{0.30 \, \text{N}}{0.156 \, \text{kg}}\right) s\]
\[0 = 324 + 3.84615 \, \text{m/s}^2 \cdot s\]
Solving for \(s\):
\[s = \frac{-324}{3.84615} \, \text{m/s}^2\]
\[s \approx -84 \, \text{m}^2/\text{s}^2\]
Since distance cannot be negative, it means that the puck will slide for approximately 84 meters before coming to rest.
To find the distance the hockey puck will slide before coming to rest, we need to use the equation for work done by friction. The work done by friction is equal to the force of friction multiplied by the distance traveled.
The equation for work is:
Work = Force × Distance
In this case, the force of friction is given as 0.30 N. The distance traveled is what we need to find.
We can rearrange the equation to solve for distance:
Distance = Work / Force
The work done by friction can be calculated using the equation:
Work = Kinetic Energy final - Kinetic Energy initial
The initial kinetic energy of the hockey puck can be calculated using the equation:
Kinetic Energy initial = 1/2 × mass × (velocity initial)^2
Substituting the given values:
Mass = 156 g = 0.156 kg (convert to kg)
Velocity initial = 18 m/s
Kinetic Energy initial = 1/2 × 0.156 kg × (18 m/s)^2
Next, we need to consider that the final kinetic energy is 0 because the hockey puck comes to rest. Therefore, the work done by friction can be expressed as:
Work = Kinetic Energy final - Kinetic Energy initial
Work = 0 - Kinetic Energy initial
Now we can substitute the values into the equations and calculate:
Work = 0 - Kinetic Energy initial
Distance = Work / Force
Distance = (0 - (1/2 × 0.156 kg × (18 m/s)^2)) / 0.30 N
Performing the calculations will give you the distance the hockey puck slides before coming to rest.