A grocery shopper tosses a(n) 9.1 kg bag of
rice into a stationary 17.6 kg grocery cart.
The bag hits the cart with a horizontal speed
of 7.0 m/s toward the front of the cart.
What is the final speed of the cart and bag?
Answer in units of m/s.
M1 = 9.1kg, V1 = 7m/s.
M2 = 17.6kg, V2 = 0.
V = Velocity after collision.
Momentum before = Momentum after
M1*V1 + M2*V2 = M1*V + M2*V,
9.1*7 + 17.6*0 = 9.1V + 17.6V,
63.7 = 26.7V,
V =
Well, if you're talking about a bag of rice hitting a grocery cart, that's one way to spice up your shopping experience! Now, let's calculate the final speed of the cart and the bag.
To solve this problem, we can use the law of conservation of momentum. The initial momentum will be equal to the final momentum.
The initial momentum of the bag can be calculated using the formula:
Initial momentum = mass of the bag x initial velocity of the bag
Let's substitute the given values:
Initial momentum of the bag = 9.1 kg x 7.0 m/s
Now, the initial momentum of the cart will be zero since it is stationary.
Since momentum is conserved, the final momentum of the system (bag + cart) will be equal to the initial momentum of the bag.
Final momentum = initial momentum of the bag
So, the final momentum of the system will be:
Final momentum = 9.1 kg x 7.0 m/s
Now, we need to find the final velocity of the system. Since the final momentum is equal to the initial momentum of the bag, we can calculate the final velocity by dividing the final momentum by the total mass of the system (bag + cart).
Let's substitute the values:
Final velocity = Final momentum / (mass of the bag + mass of the cart)
Final velocity = (9.1 kg x 7.0 m/s) / (9.1 kg + 17.6 kg)
Now, let's solve for the final velocity.
To find the final speed of the cart and bag, we can apply the law of conservation of momentum.
The momentum before the collision is equal to the momentum after the collision:
(mass of bag * velocity of bag) + (mass of cart * velocity of cart) = (total mass of system * final velocity)
Let's calculate:
mass of bag = 9.1 kg
velocity of bag = 7.0 m/s (horizontal speed towards the front of the cart)
mass of cart = 17.6 kg
velocity of cart = 0 m/s (stationary)
(total mass of system) = (mass of bag) + (mass of cart) = 9.1 kg + 17.6 kg = 26.7 kg
Using the conservation of momentum equation, we can solve for the final velocity of the system:
(9.1 kg * 7.0 m/s) + (17.6 kg * 0 m/s) = (26.7 kg * final velocity)
63.7 kg·m/s = 26.7 kg * final velocity
Dividing both sides by 26.7 kg:
final velocity = 63.7 kg·m/s / 26.7 kg
final velocity = 2.390 m/s
Therefore, the final speed of the cart and bag is approximately 2.390 m/s.
To find the final speed of the cart and bag, we can use the principle of conservation of momentum.
The momentum of an object is the product of its mass and velocity. In this case, we have a bag of rice with a mass of 9.1 kg and a horizontal velocity of 7.0 m/s, and a grocery cart with a mass of 17.6 kg and an initial velocity of 0 m/s.
According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision.
The initial momentum (before the collision) is given by:
Initial momentum = (Mass of the bag) * (Velocity of the bag) + (Mass of the cart) * (Velocity of the cart)
Since the cart is initially at rest, the initial momentum is:
Initial momentum = (Mass of the bag) * (Velocity of the bag) + (Mass of the cart) * (0)
The final momentum (after the collision) is given by:
Final momentum = (Mass of the bag + Mass of the cart) * (Final velocity)
According to the conservation of momentum, the initial momentum should be equal to the final momentum:
(Mass of the bag) * (Velocity of the bag) = (Mass of the bag + Mass of the cart) * (Final velocity)
Let's substitute the given values:
(9.1 kg) * (7.0 m/s) = (9.1 kg + 17.6 kg) * (Final velocity)
Simplifying the equation:
63.7 kg*m/s = 26.7 kg * (Final velocity)
To find the final velocity, divide both sides of the equation by 26.7 kg:
Final velocity = 63.7 kg*m/s / 26.7 kg
Final velocity ≈ 2.38 m/s
Therefore, the final speed of the cart and bag is approximately 2.38 m/s.