A 2 kg cart rolls across the floor and runs into the wall and sticks. Before the collision the cart has a velocity of 4 m/s in the x direction. The collision took place in 0.1 s.
1) What was the cart's momentum before the collision?
2) What was the cart's KE before the collision?
3) What was the momentum after the collision?
4)What was the change in the cart's momentum?
5) What was the impulse delivered to the car by the wall?
6) What was the average force exerted on the wall by the car?
PLEASE HELP ME!!!
its a direct answer.
I'd be happy to help you with these questions step by step! Here are the answers you're looking for:
1) The cart's momentum before the collision can be calculated using the formula: momentum = mass x velocity. Therefore, the momentum of the cart before the collision is 2 kg x 4 m/s = 8 kg·m/s.
2) The kinetic energy (KE) of the cart before the collision can be calculated using the formula: KE = 0.5 x mass x velocity^2. Hence, the KE of the cart before the collision is 0.5 x 2 kg x (4 m/s)^2 = 16 J.
3) Since the cart sticks to the wall after the collision, its momentum after the collision is 0 kg·m/s. This is because its velocity becomes zero after sticking to the wall.
4) The change in momentum can be calculated as the difference between the momentum before and after the collision. Therefore, the change in momentum is 8 kg·m/s - 0 kg·m/s = 8 kg·m/s.
5) Impulse is given by the formula: Impulse = change in momentum. Thus, the impulse delivered to the cart by the wall is 8 kg·m/s.
6) Average force is given by the formula: average force = change in momentum / time. Therefore, the average force exerted on the wall by the cart is 8 kg·m/s / 0.1 s = 80 N.
I hope this helps! Let me know if you have any further questions.
Of course! I'm here to help you. Let's tackle each question one by one:
1) The momentum of an object is defined as the product of its mass and velocity. In this case, the mass of the cart is given as 2 kg, and its velocity before the collision is 4 m/s in the x direction. Therefore, the momentum before the collision is calculated as:
Momentum = Mass x Velocity
Momentum = 2 kg x 4 m/s
Momentum = 8 kg⋅m/s
So, the cart's momentum before the collision is 8 kg⋅m/s.
2) The kinetic energy (KE) of an object is given by the formula KE = (1/2)mv^2, where m is the mass and v is the velocity of the object. In this case, we know the mass of the cart is 2 kg, and its velocity before the collision is 4 m/s in the x direction. Plugging these values into the formula, we get:
KE = (1/2) x 2 kg x (4 m/s)^2
KE = (1/2) x 2 kg x 16 m^2/s^2
KE = 16 J
So, the cart's kinetic energy before the collision is 16 Joules.
3) Since the cart sticks to the wall after the collision, its final velocity is 0 m/s. Therefore, the momentum after the collision can be calculated as:
Momentum = Mass x Velocity
Momentum = 2 kg x 0 m/s
Momentum = 0 kg⋅m/s
So, the cart's momentum after the collision is 0 kg⋅m/s.
4) The change in momentum is calculated by subtracting the initial momentum from the final momentum. In this case, the initial momentum was 8 kg⋅m/s (as calculated in question 1) and the final momentum was 0 kg⋅m/s (as calculated in question 3). Therefore, the change in momentum is:
Change in Momentum = Final Momentum - Initial Momentum
Change in Momentum = 0 kg⋅m/s - 8 kg⋅m/s
Change in Momentum = -8 kg⋅m/s
So, the change in the cart's momentum is -8 kg⋅m/s.
5) The impulse delivered to an object can be calculated using the equation:
Impulse = Change in Momentum
In this case, the change in momentum was calculated as -8 kg⋅m/s. So, the impulse delivered to the cart by the wall is also -8 kg⋅m/s.
6) The average force exerted on an object can be calculated using the equation:
Impulse = Force x Time
In this case, we know the impulse (-8 kg⋅m/s) and the time of impact (0.1 s). Plugging these values into the equation, we can find the average force:
-8 kg⋅m/s = Force x 0.1 s
Solving for Force:
Force = -8 kg⋅m/s / 0.1 s
Force = -80 N
So, the average force exerted on the wall by the cart is -80 Newtons.
I hope this explanation helps you understand how to solve each question step by step. If you have any further questions, feel free to ask!
1) p=mv=2•4= 8 kg•m/s
2) KE=mv²/2
3) At elastic collision
p= - mv
4) Δp= p1-(-p2) =mv – (-mv)= 2mv
5) p(wall)= Δp=2mv
6) F•Δt=mv
F= mv/ Δt