Horizontal Pulley Question [Forces]

[harujina]

Homework Statement

An object is hanging by a [mass-less] string on a [mass-less] pulley from a cart on a desk with a mass of 1.8 kg. The cart has an acceleration of 2.5 m/s^2. Calculate the mass of the hanging object given that:

a) There is no friction.
b) There is a frictional force of 0.4 N on the wheels of the cart.

Homework Equations

Fnet = ma

The Attempt at a Solution

m1 = 1.8 kg
a = 2.5 m/s^2
m2 = ?

I don't know where to start with this question...
Maybe Fnet = (1.8 kg)(2.5 m/s^2) = 4.5 N ? But what would I do with this.
... I don't know.

 

[Bryson]

What do you think the acceleration of the falling object is?

 

[harujina]

Isn't it the same?

 

[Bryson]

Perhaps, think about a force diagram. You have one force going downward and one upward. Draw it out, then solve for your unknown.

 

[Nickie]

I can provide a response to this content by first acknowledging that this is a problem involving forces and acceleration. The given information includes the mass of the cart and its acceleration, as well as the fact that the pulley and string are mass-less. This means that we can assume the mass of the cart and pulley are negligible and can be ignored in our calculations.

To solve this problem, we can use the equation Fnet = ma, where Fnet is the net force acting on the system, m is the mass of the object, and a is the acceleration. In this case, the net force is equal to the weight of the hanging object, which can be calculated using the formula Fg = mg, where g is the acceleration due to gravity (9.8 m/s^2).

a) In the first scenario, where there is no friction, the only force acting on the system is the weight of the hanging object. Therefore, we can set Fnet equal to Fg and solve for the mass of the object (m2).

Fnet = Fg = mg
m2 = Fg/g = (1.8 kg)(2.5 m/s^2)/9.8 m/s^2 ≈ 0.46 kg

b) In the second scenario, where there is a frictional force of 0.4 N on the wheels of the cart, we need to take this force into account in our calculations. The frictional force acts in the opposite direction of the motion of the cart, so it will reduce the net force acting on the system.

Fnet = Fg - Ff = ma
m2 = (Fg - Ff)/a = [(1.8 kg)(2.5 m/s^2) - 0.4 N]/2.5 m/s^2 ≈ 0.45 kg

Therefore, the mass of the hanging object in this scenario is slightly less than in the first scenario due to the presence of friction.

In conclusion, as a scientist, I can provide a response by using the appropriate equations and taking into account all given information to solve the problem. It is important to understand the concept of forces and how they affect the motion of objects in order to successfully solve problems like this one.