A hockey puck has a mass of 0.126 kg and is at rest. A hockey player makes a shot, exerting a constant force of 32.5 N on the puck for 0.16 s. With what speed does it head toward the goal?
Well, it looks like that hockey player really gave that puck a good push! Let's calculate how fast it'll be heading towards the goal.
To find the velocity of the puck, we need to use Newton's second law of motion, which states that force is equal to mass times acceleration (F = ma). In this case, the force exerted by the player is 32.5 N and the mass of the puck is 0.126 kg.
First, we need to calculate the acceleration of the puck using Newton's second law. The formula for acceleration is a = F/m, where a is the acceleration, F is the force, and m is the mass.
a = 32.5 N / 0.126 kg
a ≈ 258.73 m/s^2
Next, we need to find the change in velocity of the puck. We can use the formula v = at, where v is the change in velocity, a is the acceleration, and t is the time.
v = 258.73 m/s^2 × 0.16 s
v ≈ 41.4 m/s
So, the puck will be heading towards the goal at a speed of approximately 41.4 m/s. That's pretty fast! I hope the goalie is ready for that shot!
To find the speed of the puck heading toward the goal, we can use Newton's second law of motion and the equation for average acceleration:
F = ma,
where F is the force exerted on the puck, m is the mass of the puck, and a is the average acceleration of the puck.
Since the force is applied for a short period of time, we can also use the following equation:
F = Δp/Δt,
where Δp is the change in momentum and Δt is the change in time.
Since the puck is initially at rest, the change in momentum is equal to the final momentum. Therefore,
Δp = mv,
where v is the final velocity of the puck.
We can rearrange this equation to solve for v:
v = Δp/m.
Now, let's calculate the final velocity of the puck using these equations:
Δp = F * Δt,
v = Δp/m.
Given:
m = 0.126 kg (mass of the puck),
F = 32.5 N (force applied on the puck),
Δt = 0.16 s (time period for which the force is applied).
Substituting these values into the equations, we get:
Δp = F * Δt = 32.5 N * 0.16 s = 5.2 N·s,
v = Δp/m = (5.2 N·s) / (0.126 kg) ≈ 41.27 m/s.
Therefore, the speed at which the puck heads toward the goal is approximately 41.27 m/s.
To find the speed at which the hockey puck heads toward the goal, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, we need to find the acceleration of the hockey puck. We can use the formula:
Acceleration = Force / Mass
Given:
Mass of the puck (m) = 0.126 kg
Force exerted by the player (F) = 32.5 N
Substituting the given values into the formula:
Acceleration = 32.5 N / 0.126 kg
Calculating the acceleration:
Acceleration = 258.7 m/s^2
Next, we can proceed to determine the final velocity of the puck by using the equation that relates acceleration, time, and initial velocity:
Final velocity = Initial velocity + (Acceleration * Time)
Since the puck is initially at rest, the initial velocity (Initial velocity) is 0 m/s.
Given:
Time (t) = 0.16 s
Acceleration (a) = 258.7 m/s^2
Initial velocity (u) = 0 m/s
Substituting the given values into the formula:
Final velocity = 0 m/s + (258.7 m/s^2 * 0.16 s)
Calculating the final velocity:
Final velocity = 41.392 m/s
Therefore, the hockey puck heads towards the goal with a speed of approximately 41.392 m/s.
F=ma=mΔv/Δt=m(v2-v1)/Δt
As v1=0
v2=FΔt/m=32.5x0.16/0.126=41.3m/s