# Dynamics - frames of reference

In summary: Actually, you can do the calculation without M0 and m1. The acceleration is simply [itex]\mu(m0+m1)a= (m0+m1)g.

## Homework Statement

here:
http://img144.imageshack.us/img144/7518/26700576ok1.gif

## The Attempt at a Solution

well, I tried to solve the motion equation from the inside table. I think there should be a d'elambertian force to the left, and friction force to the right, so:
Fd - miu*N = m1*a . Now, I am not sure about the Normal force- need it be N=m1+m2, or just m1 (I think it's the first option).
Then my main problem - about the d'elambertian force: Is the Fd equal to the external frame's F, or are the accelerations equal, and the forces need to be calculated via the acceleration and masses?
And finally: when I try to calculate on the external frame (the cart): need the motion equation be equaled to just Ma, or all the masses, ie (m1+m2+M)a ?

Last edited by a moderator:
anyone?

Actually, there are two different situations to think about. If the force is applied to the cart at t= 0, then, since there is friction between the cart and the table will start moving as well as the cart. Since there is NO friction between the table and m2, m2 will NOT start moving. Eventually, it will just slide off the table and fall onto the floor of the cart. But while it is on the table, it contributes to the normal force the table makes with the floor of the cart: the normal force is (m1+ m2)g so the friction force exerted by the table on the cart is [itex]\mu(m1+ m2)g= 0.8(1+ 9)(9.81)= 8(9.81)= 78.48 N. The Net force 1120- 78.48= 1041.52 N. Since the total mass of the cart is M0+ m1= 81 kg (you do NOT count m2 since it is not being accelerated) The carts acceleration is 1041.52/81= 12.8 m/s2.

The other situation is after m1 has slid off the table. It no longer contributes to the normal force increasing the friction force of the table on the floor of the cart but might contribute to the total mass if there is friction between it and the floor of the cart.

Thanks for the thorough response!

HallsofIvy said:
Actually, there are two different situations to think about. If the force is applied to the cart at t= 0, then, since there is friction between the cart and the table will start moving as well as the cart. Since there is NO friction between the table and m2, m2 will NOT start moving. Eventually, it will just slide off the table and fall onto the floor of the cart. But while it is on the table, it contributes to the normal force the table makes with the floor of the cart: the normal force is (m1+ m2)g so the friction force exerted by the table on the cart is [itex]\mu(m1+ m2)g= 0.8(1+ 9)(9.81)= 8(9.81)= 78.48 N. The Net force 1120- 78.48= 1041.52 N. Since the total mass of the cart is M0+ m1= 81 kg (you do NOT count m2 since it is not being accelerated) The carts acceleration is 1041.52/81= 12.8 m/s2.

The other situation is after m1 has slid off the table. It no longer contributes to the normal force increasing the friction force of the table on the floor of the cart but might contribute to the total mass if there is friction between it and the floor of the cart.

You said to include both M0 and m1 as the objects being accelerated. But, aren't they moving at different speeds? so how can I do F=(m0+m1)a, whilst m0 and m1 aren't moving together?

## 1. What is a frame of reference in dynamics?

A frame of reference in dynamics is a coordinate system used to describe the motion of an object. It is a set of axes with a fixed origin and orientation that is used to measure the position, velocity, and acceleration of an object.

## 2. How do frames of reference affect the description of motion?

Frames of reference are important in describing motion because they provide a standard for measuring the position, velocity, and acceleration of an object. Different frames of reference can result in different measurements of these quantities, so it is important to choose an appropriate frame of reference for a given situation.

## 3. What are the different types of frames of reference in dynamics?

There are two main types of frames of reference in dynamics: inertial and non-inertial. Inertial frames of reference are ones in which Newton's laws of motion hold true, while non-inertial frames are ones in which these laws do not hold true due to the presence of acceleration or rotation.

## 4. How do you choose an appropriate frame of reference for a given situation?

The choice of frame of reference depends on the specific dynamics problem being studied. In general, an inertial frame of reference is preferred as it simplifies the analysis and allows for the use of Newton's laws of motion. However, in cases where an object is accelerating or rotating, a non-inertial frame of reference may be necessary to accurately describe the motion.

## 5. Can different observers have different frames of reference?

Yes, different observers can have different frames of reference. This is known as the principle of relativity and is a fundamental concept in physics. The laws of physics should be the same for all observers, regardless of their chosen frame of reference.

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