hockey puck with a mass of 0.18 kg travels at a velocity of 40 m/s toward a goalkeeper. The goalker mass of 120 kg and is at rest. Assuming a closed system, find the total momentum of the goalkeeper after the puck is caught by the goalkeeper.
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum before an event is equal to the total momentum after the event.
Before the puck is caught by the goalkeeper, the total momentum of the system is given by the sum of the momentum of the puck and the goalkeeper.
The momentum of an object is calculated by multiplying its mass by its velocity.
The momentum of the puck is:
momentum of the puck = mass of the puck × velocity of the puck
momentum of the puck = 0.18 kg × 40 m/s
The momentum of the goalkeeper is:
momentum of the goalkeeper = mass of the goalkeeper × velocity of the goalkeeper
momentum of the goalkeeper = 120 kg × 0 m/s (since the goalkeeper is at rest initially)
The total momentum before the puck is caught is:
total momentum before = momentum of the puck + momentum of the goalkeeper
To find the total momentum after the puck is caught, we need to consider that the goalkeeper catches the puck and is set into motion in the opposite direction with the same speed.
Since momentum is a vector quantity, it has both magnitude and direction.
When the goalkeeper catches the puck, the puck's momentum changes direction but not magnitude. Therefore, its momentum after being caught is equal in magnitude to its momentum before being caught but in the opposite direction.
Similarly, the goalkeeper's momentum also changes direction but not magnitude. Therefore, the goalkeeper's momentum after catching the puck is equal in magnitude to the puck's momentum before being caught but in the same direction.
So the total momentum after the puck is caught is:
total momentum after = -momentum of the puck + momentum of the goalkeeper
Since the puck's momentum is in the opposite direction, its sign is negative.
Substituting the values, we have:
total momentum after = -(0.18 kg × 40 m/s) + (120 kg × 40 m/s)
Calculating this expression, we find:
total momentum after = -7.2 kg·m/s + 4800 kg·m/s
Simplifying further, we get:
total momentum after = 4792.8 kg·m/s
Therefore, the total momentum of the goalkeeper after the puck is caught is 4792.8 kg·m/s.
To find the total momentum of the goalkeeper after the puck is caught by the goalkeeper, we can use the law of conservation of momentum, which states that the total momentum before an event is equal to the total momentum after the event in a closed system.
The momentum of an object is calculated by multiplying its mass (m) by its velocity (v).
Momentum (p) = mass (m) * velocity (v)
The momentum of the hockey puck before it is caught by the goalkeeper is given by:
Momentum of puck (puck) = mass of puck (m_puck) * velocity of puck (v_puck)
The momentum of the goalkeeper before the puck is caught is given by:
Momentum of goalkeeper (goalkeeper) = mass of goalkeeper (m_goalkeeper) * velocity of goalkeeper (v_goalkeeper)
Since the goalkeeper is at rest before the catch, the velocity of the goalkeeper (v_goalkeeper) is zero.
According to the law of conservation of momentum, the total momentum before the catch (puck + goalkeeper) should be equal to the total momentum after the catch.
Therefore, the total momentum of the goalkeeper after the puck is caught will be equal to the momentum of the puck before the catch.
Total momentum of goalkeeper after the catch = Momentum of puck before the catch
So, the total momentum of the goalkeeper after the puck is caught by the goalkeeper will be:
Total momentum of goalkeeper (after catch) = mass of puck * velocity of puck
Given:
Mass of puck (m_puck) = 0.18 kg
Velocity of puck (v_puck) = 40 m/s
Total momentum of goalkeeper (after catch) = 0.18 kg * 40 m/s
Total momentum of goalkeeper (after catch) = 7.2 kg·m/s
Therefore, the total momentum of the goalkeeper after the puck is caught by the goalkeeper is 7.2 kg·m/s.
To find the total momentum of the goalkeeper after the puck is caught, we need to use the law of conservation of momentum, which states that the total momentum before an event is equal to the total momentum after the event in a closed system.
The momentum of an object is defined as the product of its mass and velocity, given by the equation:
Momentum = mass × velocity
Let's calculate the initial momentum of the puck using the given information:
Mass of the puck (m1) = 0.18 kg
Velocity of the puck (v1) = 40 m/s
Initial momentum of the puck (P1) = m1 × v1
= 0.18 kg × 40 m/s
= 7.2 kg·m/s (to two decimal places)
Since the goalkeeper is at rest initially, the initial momentum of the goalkeeper (P2) is 0 kg·m/s.
According to the law of conservation of momentum, the total momentum before catching the puck is equal to the total momentum after catching it:
Total initial momentum = Total final momentum
P1 + P2 = P' (where P' is the total momentum after catching the puck)
Since P2 is 0, the equation simplifies to:
P1 = P'
Therefore, the total momentum of the goalkeeper after catching the puck is 7.2 kg·m/s.