1....How much force needed to bring a 3200 lb car from rest to a velocity of 44 m/s in 8 sec.?
2....A ball with a mass of 2 kg move to the right with a speed of 2 m/s. It hits a ball of mass 0.50 kg which is at rest. After collision the second ball moves to the right with a speed of 1 m/s. What happens to the first ball?...Suppose that the 2 balls stick together moves as one after collision, what is their final velocity?
1. Force*time=changemomentum
2. Momentum is conserved.
1. Impulse = force x time
= momentum change
Apply the formula
2. Total momentum remains the same.
In the second case,
M1* (2 m/s) = (M1 + M2)*Vfinal
Vfinal = (2/2.5)* 2 m/s = __
Try doing the first case yourself. Make sure + is right and - is left for velocity.
1. To calculate the force required to accelerate the car, we can use Newton's second law of motion which states that force is equal to mass multiplied by acceleration (F = ma). In this case, we need to find the acceleration first.
The initial velocity (u) of the car is 0 m/s since it is at rest. The final velocity (v) is given as 44 m/s, and the time taken (t) is 8 seconds. We can use the equation v = u + at to find the acceleration (a).
v = u + at
44 = 0 + a * 8
44 = 8a
a = 44 / 8
a = 5.5 m/s²
Now that we have the acceleration, we can calculate the force using the formula F = ma.
F = 3200 lb * 5.5 m/s²
Note: We need to convert the weight of the car from lb to kg. 1 lb = 0.454 kg.
F = 3200 lb * 0.454 kg/lb * 5.5 m/s²
F ≈ 7840 N
Therefore, approximately 7840 Newtons of force is needed to bring the car to a velocity of 44 m/s in 8 seconds.
2. In this scenario, we can use the principle of conservation of momentum to analyze the collision between the two balls.
Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces are acting on the system.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v). Therefore, the momentum before the collision is as follows:
Momentum of the first ball = mass of the first ball * velocity of the first ball = 2 kg * 2 m/s = 4 kg·m/s
Momentum of the second ball = mass of the second ball * velocity of the second ball = 0.50 kg * 0 m/s = 0 kg·m/s
Since the second ball is initially at rest, its momentum is zero.
After the collision, the two balls stick together and move as one. Let's denote their final velocity by V (V is the common velocity after collision).
According to the conservation of momentum, the total momentum before the collision equals the total momentum after the collision:
Total momentum before collision = Total momentum after collision
(2 kg * 2 m/s) + (0.50 kg * 0 m/s) = (2 kg + 0.50 kg) * V
4 kg·m/s = 2.5 kg * V
Dividing both sides by 2.5 kg:
V = 4 kg·m/s / 2.5 kg
V = 1.6 m/s
Therefore, if the two balls stick together and move as one after the collision, their final velocity would be 1.6 m/s to the right.