Can you show work please..?
1. Joe is sledding down a snow hill when he collides with Mike half way down the hill. Joe and the sled have a mass of 65 kg and their velocity before the collision was 12 m/s. If Mike has a mass of 55 kg, what velocity would Joe, Mike, and the sled have after the collision?
2. A 3 kg cart is moving along when it strikes a 2 kg cart (initially at rest). The velocity of the two-cart combination after the collision is 4 m/s. Calculate the velocity of the 3 kg cart before the collision.
3. Tyler is standing at the 10-yard line waiting to catch the initial kick-off. The .75 kg football experiences a change in velocity of 12 m/s in .17 s when caught by Tyler. What force does Tyler apply on the football?
1) assuming they stuck together after the collision?
Assuming that, momentum is conserved.
momentum before= momentum after
65*12+0=(65+55)V solve for V
Certainly! I will show the work for each of the questions.
1. To solve this problem, we can use the law of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity. Therefore, the momentum before the collision can be calculated as follows:
Momentum before collision = (mass of Joe and sled) * (initial velocity of Joe and sled)
= (65 kg) * (12 m/s)
= 780 kg·m/s
Since the momentum is conserved, the total momentum after the collision will also be equal to 780 kg·m/s. After the collision, Joe, Mike, and the sled will move as a single system. Let's assume their final velocity after the collision is v.
The total mass of Joe, Mike, and the sled is 65 kg + 55 kg = 120 kg. Therefore, the momentum after the collision can be calculated as:
Momentum after collision = (total mass of Joe, Mike, and sled) * (final velocity)
= (120 kg) * (v)
Since the total momentum before and after the collision is the same, we can set the two equations equal to each other:
Momentum before collision = Momentum after collision
780 kg·m/s = (120 kg) * (v)
Now we can solve for v:
v = 780 kg·m/s / (120 kg)
v ≈ 6.5 m/s
Therefore, Joe, Mike, and the sled will have a velocity of approximately 6.5 m/s after the collision.
2. To solve this problem, we can again use the law of conservation of momentum. The initial momentum of the system is the momentum of the 3 kg cart, and the final momentum is the momentum of the two-cart combination.
Let's assume the velocity of the 3 kg cart before the collision is u. The initial momentum of the system can be calculated as:
Initial momentum = (mass of 3 kg cart) * (initial velocity of 3 kg cart)
= (3 kg) * (u)
The final momentum of the system is equal to the momentum of the two-cart combination after the collision, which is given as follows:
Final momentum = (mass of 3 kg cart + mass of 2 kg cart) * (final velocity of two-cart combination)
= (3 kg + 2 kg) * (4 m/s)
= 5 kg * 4 m/s
= 20 kg·m/s
Since the momentum is conserved, we can set the initial momentum equal to the final momentum and solve for u:
(3 kg) * (u) = 20 kg·m/s
u = 20 kg·m/s / 3 kg
u ≈ 6.67 m/s
Therefore, the velocity of the 3 kg cart before the collision is approximately 6.67 m/s.
3. To solve this problem, we can use Newton's second law of motion, which states that the force acting on an object is equal to the rate of change of its momentum.
The change in momentum of the football can be calculated as follows:
Change in momentum = (mass of the football) * (change in velocity)
= (0.75 kg) * (12 m/s)
Now, we need to determine the time it took for the change in velocity to occur. In the problem, it is given that the change in velocity happens in 0.17 s.
Using Newton's second law, we can calculate the force applied by Tyler on the football:
Force = Change in momentum / Time
= (0.75 kg * 12 m/s) / 0.17 s
Simplifying the equation, we get:
Force ≈ 53.24 N
Therefore, Tyler applies approximately 53.24 Newtons of force on the football.