A cart traveling at 0.3 m/s collides with stationary object. After the collision, the cart rebounds in the opposite direction. The same cart again traveling at 0.3 m/s collides with a different stationary object. This time the cart is at rest after the collision. In which collision is the impulse on the cart greater?
A. The first collision.
B. Cannot be determined without knowing the rebound speed of the first collision.
C. The second collision.
D. Cannot be determined without knowing the mass of the cart.
E. The impulses are the same.
To determine which collision has a greater impulse on the cart, we need to understand the concept of impulse. Impulse is the change in momentum of an object and is calculated using the equation:
Impulse = change in momentum
Momentum is defined as the product of an object's mass and its velocity:
Momentum = mass × velocity
In the first collision, the cart is moving with a velocity of 0.3 m/s and then rebounds in the opposite direction. This means that the initial velocity is positive and the final velocity is negative.
Let's consider the momentum before and after the collision:
Before the collision: momentum = mass × 0.3 m/s (positive because of the direction)
After the collision: momentum = mass × (-0.3 m/s) (negative because of the opposite direction)
The change in momentum, and therefore the impulse for the first collision, is given by the difference between the two momenta:
Impulse for first collision = (mass × (-0.3 m/s)) - (mass × 0.3 m/s)
= -0.6 × mass
In the second collision, the cart is again moving with a velocity of 0.3 m/s, but this time it comes to rest after the collision. This means that the initial velocity is positive, and the final velocity is 0 m/s.
Let's consider the momentum before and after the collision:
Before the collision: momentum = mass × 0.3 m/s (positive)
After the collision: momentum = mass × 0 m/s (zero because the cart is at rest)
The change in momentum, and therefore the impulse for the second collision, is given by the difference between the two momenta:
Impulse for second collision = (mass × 0 m/s) - (mass × 0.3 m/s)
= 0 - 0.3 × mass
Comparing the two impulses, we can see that:
Impulse for first collision = -0.6 × mass
Impulse for second collision = -0.3 × mass
Since -0.6 is greater in magnitude than -0.3, we can conclude that the impulse on the cart is greater in the first collision.
Therefore, the answer is A. The impulse on the cart is greater in the first collision.