You are given a four-wheeled cart of mass 11 kg, where the distance between a wheel and its nearest neighbors is 2.1 m. Suppose we load this cart with a crate of mass 109 kg, where the crate's center of mass is located in the back-middle of the cart, 0.525 m from its center.
a) Find the weight on the nearer wheels of the cart under this load.
b) Find the weight on the farther wheels of the cart under this load.
To find the weight on the nearer and farther wheels of the cart, we need to consider the distribution of the total weight of the cart and the crate.
a) Weight on the nearer wheels of the cart:
The nearest wheels to the crate's center of mass are the front wheels. Since there are two front wheels on the cart, we need to divide the weight of the crate evenly between them.
The weight on each nearer wheel can be calculated using the formula:
Weight on each front wheel = (mass of crate / number of front wheels) * acceleration due to gravity
Given:
Mass of the crate = 109 kg
Number of front wheels = 2 (since there are two front wheels)
Plugging in the values, we get:
Weight on each front wheel = (109 kg / 2) * 9.8 m/s^2
b) Weight on the farther wheels of the cart:
The farther wheels from the crate's center of mass are the back wheels. Similar to the front wheels, we divide the weight of the crate evenly between the two back wheels.
The weight on each farther wheel can be calculated using the same formula as for the front wheels:
Weight on each back wheel = (mass of crate / number of back wheels) * acceleration due to gravity
Given:
Number of back wheels = 2 (since there are two back wheels)
Plugging in the values, we get:
Weight on each back wheel = (109 kg / 2) * 9.8 m/s^2
So, the answer to the question is:
a) The weight on each of the nearer wheels of the cart under this load is (109 kg / 2) * 9.8 m/s^2
b) The weight on each of the farther wheels of the cart under this load is (109 kg / 2) * 9.8 m/s^2