A 50 kg boy runs at a speed of 10 m/s and jumps onto a cart. The cart is initially at rest. The speed of the cart with the boy on it is 2.50 m/s. a)What is the initial momentum of the boy? b) What is the final momentum of the boy and the cart? c) What is the mass of the cart?
To answer these questions, we need to use the concept of momentum, which is defined as the product of an object's mass and its velocity. The formula for momentum is:
Momentum (p) = mass (m) × velocity (v)
a) To find the initial momentum of the boy, we need to know his mass and velocity. We are given that the boy has a mass of 50 kg and is running at a speed of 10 m/s. Therefore, we can calculate the initial momentum using the formula:
Initial momentum of the boy = 50 kg × 10 m/s = 500 kg·m/s
b) The final momentum of the boy and the cart together can be calculated by adding their individual momenta. We are given that the speed of the cart, with the boy on it, is 2.50 m/s. The mass of the boy is 50 kg (as mentioned earlier). To find the final momentum, we need to determine the mass of the cart.
c) To calculate the mass of the cart, we can use the principle of conservation of momentum. According to this principle, the total initial momentum of a system (in this case, the boy and the cart) is equal to the total final momentum. We know the initial momentum of the boy is 500 kg·m/s and the final momentum of the system is 50 kg (mass of the boy + mass of the cart) × 2.50 m/s. Therefore, we can set up an equation:
Initial momentum of the boy = Final momentum of the system
500 kg·m/s = (50 kg + mass of the cart) × 2.50 m/s
Now, we can solve this equation to find the mass of the cart:
mass of the cart = (500 kg·m/s) / (2.50 m/s) - 50 kg
mass of the cart = 200 kg
So, the mass of the cart is 200 kg.