a hockey stick has a mechanical advantage of 4. if the effort arm(which is the distance between the fulcrum and your pushing hand-effort)is 25cm long, how long is the stick? if your hand is pushing at a speed of 20km/h, how fast will the puck move?
the answer is 2million. i hope i was fast enough to help you
p.s you asked this question before i was born
Oh, I see we've got a curious hockey enthusiast here! Let's solve this riddle with a touch of humor, shall we?
Now, if a hockey stick has a mechanical advantage of 4 and the effort arm is 25cm long, we can use a simple formula to find out the total length of the stick. Just divide the length of the stick by the effort arm and ta-da, you've got your answer!
So, with my math skills in tip-top shape and my clown nose on tight, I calculate that the hockey stick must be 100cm long. That's quite a stick, eh?
Now, when it comes to how fast the puck will move, it depends on many factors. The speed of your hand is irrelevant here, my friend, as it's the force you apply that determines the puck's speed. So, let's crack a joke while we break this down!
Why did the puck go to comedy school? It wanted to master the art of being "puck"ular!
In all seriousness, the speed of the puck depends on various factors like the force applied, the mass of the puck, and external factors like friction. Without knowing these details, it's hard to give a precise answer. So, let's just say the puck will move as fast as it can while maintaining its dignity on the ice.
To find the length of the hockey stick, we can use the formula of mechanical advantage:
Mechanical Advantage = Length of the Stick / Length of the Effort Arm
Given that the mechanical advantage is 4 and the length of the effort arm is 25 cm.
4 = Length of the Stick / 25 cm
Rearranging the equation, we get:
Length of the Stick = Mechanical Advantage * Length of the Effort Arm
Length of the Stick = 4 * 25 cm
Length of the Stick = 100 cm
Therefore, the length of the hockey stick is 100 cm.
Now, let's calculate how fast the puck will move. We can use the principle of conservation of energy, assuming there are no other external forces acting on the system.
The work done by your hand pushing the stick is equal to the work done to move the puck:
Work = Force × Distance
The force you apply to the stick is determined by your speed. Since the speed is given in km/h, we need to convert it to m/s:
20 km/h = 20,000 m/60 min × 1 min/60 s = 20/3 m/s
Now, we can substitute the values into the equation:
Work done by your hand = Force × Distance
Work done by your hand = Force × (Length of the Stick + Length of the Effort Arm)
Since the mechanical advantage is defined as the ratio of the force applied by the stick to the force applied by your hand, we can write:
Force applied by your hand = Force applied by the stick / Mechanical Advantage
Therefore, the work done by your hand can be rewritten as:
Work done by your hand = (Force applied by the stick / Mechanical Advantage) × (Length of the Stick + Length of the Effort Arm)
The work done by your hand is converted into kinetic energy, which is given by:
Kinetic Energy = (1/2) × Mass × (Velocity)^2
Since the work done by your hand is equal to the kinetic energy of the puck:
(Force applied by the stick / Mechanical Advantage) × (Length of the Stick + Length of the Effort Arm) = (1/2) × Mass × (Velocity)^2
We can now solve for the velocity of the puck:
Velocity = √( (2 × (Force applied by the stick / Mechanical Advantage) × (Length of the Stick + Length of the Effort Arm)) / Mass )
Since we don't have the mass of the puck given, we can't calculate the exact velocity. However, we can see that the velocity is directly proportional to the force applied by the stick and the length of the stick plus the length of the effort arm. So, increasing those values will result in higher puck velocity.
To find the length of the hockey stick, we can use the formula for mechanical advantage:
Mechanical Advantage = Length of Load Arm / Length of Effort Arm
In this case, the mechanical advantage is given as 4, and the length of the effort arm is given as 25 cm. Let's substitute those values into the formula and solve for the length of the load arm:
4 = Length of Load Arm / 25
Multiplying both sides of the equation by 25, we get:
4 * 25 = Length of Load Arm
Length of Load Arm = 100 cm
Therefore, the hockey stick is 100 centimeters long.
Moving on to the second part of your question, the speed at which the puck moves is determined by the force exerted on it. The speed of your hand alone (20 km/h) does not directly determine the speed of the puck because it depends on other factors such as the friction between the stick and the puck, the weight of the puck, and the force exerted on the puck.
However, we can say that when using a hockey stick, the force applied to the puck can be greater than the force applied by your hand alone due to the mechanical advantage of the stick. This increased force can result in a faster speed for the puck.
It's important to note that multiple factors can affect the speed of the puck in a real-world scenario, and the mechanical advantage of the stick is just one part of the equation.