1.)A 0.5 kg hockey puck moving at 35 m/s hits a straw bale, stopping in 1 s.
a) What impulse is delivered to the ball?
b) What force is exerted on the puck?
2.) A racing car with a mass of 1400 kg hits a slick spot and crashes head-on into a concrete wall at 50 m/s, coming to a halt in 0.8 s.
a) What is the change in momentum?
b) What is the impulse
c)What force is exerted on the car?
3.) An ambulance weighing 3000 kg comes racing to the rescue, hits the same slick spot, and then collides with a padded part of the wall at 50 m/s, coming to a halt in 2 s.
a) What is the change in momentum?
b) What is the impulse
c)What force is exerted on the ambulance?
d) How this answer differ from the problem above??
>>FORMULA'S<<
P=w/t
P= energy/time
P=mad/t
P= Fd/t
:)
To solve these problems, we will use the formulas related to impulse and momentum.
1a) The impulse delivered to the hockey puck is equal to the change in momentum of the puck. The formula for impulse is given as:
Impulse (J) = Change in momentum (Δp) = m * Δv,
where m is the mass of the hockey puck and Δv is the change in velocity.
Given:
Mass (m) = 0.5 kg,
Initial velocity (u) = 35 m/s,
Final velocity (v) = 0 m/s (puck comes to a stop).
The change in velocity is: Δv = v - u
= 0 m/s - 35 m/s
= -35 m/s.
So, the change in momentum is: Δp = m * Δv
= 0.5 kg * (-35 m/s)
= -17.5 kg m/s.
The impulse delivered to the hockey puck is -17.5 kg m/s. The minus sign indicates that the impulse acts in the opposite direction to the initial velocity.
1b) The force exerted on the puck can be calculated using the formula:
Force (F) = Impulse (J) / Time (t).
Given:
Impulse (J) = -17.5 kg m/s (from part a),
Time (t) = 1 s (time taken to stop).
Using the formula, F = -17.5 kg m/s / 1 s,
= -17.5 N.
Therefore, the force exerted on the puck is -17.5 Newtons. The minus sign indicates that the force acts in the opposite direction to the initial velocity.
2a) The change in momentum of the racing car can be calculated using the formula mentioned earlier:
Change in momentum (Δp) = m * Δv,
where m is the mass of the car, and Δv is the change in velocity.
Given:
Mass (m) = 1400 kg,
Initial velocity (u) = 50 m/s,
Final velocity (v) = 0 m/s (car comes to a halt).
The change in velocity is: Δv = v - u
= 0 m/s - 50 m/s
= -50 m/s.
So, the change in momentum is: Δp = m * Δv
= 1400 kg * (-50 m/s)
= -70,000 kg m/s.
The change in momentum of the racing car is -70,000 kg m/s.
2b) The impulse experienced by the car is equal to the change in momentum and can be calculated using the formula:
Impulse (J) = Change in momentum (Δp).
Given:
Change in momentum (Δp) = -70,000 kg m/s (from part a).
Therefore, the impulse experienced by the racing car is -70,000 kg m/s.
2c) The force exerted on the car can be calculated using the formula mentioned earlier:
Force (F) = Impulse (J) / Time (t).
Given:
Impulse (J) = -70,000 kg m/s (from part b),
Time (t) = 0.8 s.
Using the formula, F = -70,000 kg m/s / 0.8 s,
= -87,500 N.
Therefore, the force exerted on the car is -87,500 Newtons.
3a) The change in momentum of the ambulance can be calculated using the same formula:
Change in momentum (Δp) = m * Δv,
where m is the mass of the ambulance and Δv is the change in velocity.
Given:
Mass (m) = 3000 kg,
Initial velocity (u) = 50 m/s,
Final velocity (v) = 0 m/s (ambulance comes to a halt).
The change in velocity is: Δv = v - u
= 0 m/s - 50 m/s
= -50 m/s.
So, the change in momentum is: Δp = m * Δv
= 3000 kg * (-50 m/s)
= -150,000 kg m/s.
The change in momentum of the ambulance is -150,000 kg m/s.
3b) The impulse experienced by the ambulance is equal to the change in momentum and can be calculated using the formula:
Impulse (J) = Change in momentum (Δp).
Given:
Change in momentum (Δp) = -150,000 kg m/s (from part a).
Therefore, the impulse experienced by the ambulance is -150,000 kg m/s.
3c) The force exerted on the ambulance can be calculated using the same formula:
Force (F) = Impulse (J) / Time (t).
Given:
Impulse (J) = -150,000 kg m/s (from part b),
Time (t) = 2 s.
Using the formula, F = -150,000 kg m/s / 2 s,
= -75,000 N.
Therefore, the force exerted on the ambulance is -75,000 Newtons.
3d) This answer is different from the problem above because the mass and time values are different for the ambulance. The different mass and time result in a different change in momentum and impulse, leading to a different force exerted on the ambulance.