A hockey goalie is standing on ice. Another player fires a puck (m = 0.22 kg) at the goalie with a velocity of +63 m/s
(a) If the goalie catches the puck with his glove in a time of 7.0 10-3 s, what is the average force (magnitude and direction) exerted on the goalie by the puck?
N
(b) Instead of catching the puck, the goalie slaps it with his stick and returns the puck straight back to the player with a velocity of +63 m/s. The puck and stick are in contact for a time of 7.0 10-3 s. Now what is the average force exerted on the goalie by the puck?
(a) Well, we have a goalie facing a speeding puck! It's like a battle between "catch me if you can" and "I've gotcha now!" To find the average force, we can use the formula:
Average force = (change in momentum) / (change in time)
The change in momentum can be calculated as:
Change in momentum = mass × (final velocity - initial velocity)
Given that the mass of the puck (m) is 0.22 kg, the initial velocity (u) is 63 m/s, and the final velocity (v) is 0 m/s (since the goalie caught the puck and brought it to a stop), we can plug these values into the formula.
Change in momentum = 0.22 kg × (0 m/s - 63 m/s)
Now, we divide this change in momentum by the time it took for the goalie to catch the puck, which is 7.0 × 10^(-3) s. Let's calculate!
Average force = (0.22 kg × (-63 m/s)) / (7.0 × 10^(-3) s)
After doing the math, we find that the average force exerted on the goalie by the puck is about 2.808 N. The negative sign indicates that the force is in the opposite direction to the initial motion of the puck, because the goalie brought it to a stop.
(b) Ah, the goalie decided not to keep the puck for himself and instead slapped it back like a tennis pro! In this case, the velocity of the puck after the slap is +63 m/s, which is the same as the initial velocity.
We can use the same formula to calculate the average force. The change in momentum is:
Change in momentum = mass × (final velocity - initial velocity)
Given that the mass of the puck is 0.22 kg, the initial velocity is 0 m/s (since the goalie was catching the puck), and the final velocity is 63 m/s (the same as the initial velocity), we can plug these values into the formula:
Change in momentum = 0.22 kg × (63 m/s - 0 m/s)
Again, let's divide this change in momentum by the time the puck and stick were in contact, which is 7.0 × 10^(-3) s.
Average force = (0.22 kg × (63 m/s - 0 m/s)) / (7.0 × 10^(-3) s)
After some calculations, we find that the average force exerted on the goalie by the puck is still approximately 2.808 N. The direction of the force remains the same as before, opposing the initial motion of the puck.
So in both cases, the goalie had to face a force of about 2.808 N. Let's hope the goalie stays strong and doesn't turn into a human slingshot!
To find the average force exerted on the goalie by the puck, we can use Newton's second law of motion, which states that force (F) is equal to the change in momentum (Δp) divided by the change in time (Δt):
F = Δp / Δt
(a) Now let's calculate the average force exerted on the goalie when he catches the puck with his glove in 7.0 × 10^-3 s.
The change in momentum (Δp) is given by the equation:
Δp = m * Δv
where m is the mass of the puck (0.22 kg) and Δv is the change in velocity.
The initial velocity of the puck is +63 m/s and the final velocity is 0 m/s when the goalie catches the puck.
Therefore, the change in velocity (Δv) = (0 m/s) - (+63 m/s) = -63 m/s.
Substituting the values into the equation for Δp:
Δp = (0.22 kg) * (-63 m/s) = -13.86 kg·m/s
Since the average force (F) is equal to Δp / Δt, we can calculate:
F = (-13.86 kg·m/s) / (7.0 × 10^-3 s)
F = -1980 N
The magnitude of the average force exerted on the goalie by the puck is 1980 N. The negative sign indicates that the force is in the opposite direction of the original velocity of the puck.
(b) Now, let's calculate the average force exerted on the goalie when he slaps the puck back with his stick in 7.0 × 10^-3 s.
The change in momentum (Δp) is still given by the equation:
Δp = m * Δv
The initial velocity of the puck is 0 m/s and the final velocity is +63 m/s when the goalie slaps the puck back.
Therefore, the change in velocity (Δv) = (+63 m/s) - (0 m/s) = +63 m/s.
Substituting the values into the equation for Δp:
Δp = (0.22 kg) * (+63 m/s) = +13.86 kg·m/s
Since the average force (F) is equal to Δp / Δt, we can calculate:
F = (+13.86 kg·m/s) / (7.0 × 10^-3 s)
F = +1980 N
The magnitude of the average force exerted on the goalie by the puck is 1980 N. The positive sign indicates that the force is in the same direction as the final velocity of the puck.
To find the average force exerted on the goalie by the puck in both scenarios, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a):
F = m * a
For part (a), since the goalie catches the puck, the puck comes to rest. So, we can calculate the acceleration of the puck using the equation:
a = (final velocity - initial velocity) / time
Given:
Mass of puck (m) = 0.22 kg
Initial velocity (u) = 63 m/s
Time (t) = 7.0 x 10^-3 s
Substituting these values into the equation, we get:
a = (0 - 63) / (7.0 x 10^-3)
a = -9000 m/s^2
Now, we can calculate the force exerted on the goalie using the formula:
F = m * a
Substituting the values:
F = 0.22 kg * -9000 m/s^2
F = -1980 N
Therefore, the average force exerted on the goalie by the puck is 1980 N in the opposite direction of the initial velocity of the puck.
For part (b), since the puck changes direction after being hit by the goalie's stick, the final velocity is also 63 m/s in the opposite direction. The acceleration can be calculated using the same formula:
a = (final velocity - initial velocity) / time
a = (63 - (-63)) / (7.0 x 10^-3)
a = 18000 m/s^2
Now, we can calculate the force exerted on the goalie using the formula:
F = m * a
Substituting the values:
F = 0.22 kg * 18000 m/s^2
F = 3960 N
Therefore, the average force exerted on the goalie by the puck when the goalie slaps it with his stick is 3960 N in the opposite direction of the initial velocity of the puck.