# Laws of Motion, vertical acceleration question.

• Bucky
In summary, the problem involves finding the actual mass and upward acceleration of a lift that is being accelerated upwards and downwards at certain rates, while a spring balance measures the weight of the mass. The spring balance measures force, not mass, and is marked with mass units assuming the use of an inertial frame of reference. After substituting the correct quantities, the equations can be solved to find the values of mass and acceleration.
Bucky
"In a lift accelerated upwards at a certain rate, a spring balance indicates a weight to have a mass of 10kg. When the lift is accelerated downwards at twice the upward rate, the mass appears to be 7kg. Find the actual mass and the upward acceleration of the lift."

In short, I am stuck. I think this question involves simultaneus equations, but i can't get a set of equations that make sense. I've looked at the textbooks I have but they all concern themselves with the resistance forces or tensions in the strings.

try to put in pseudo forces on the block

Bucky said:
"In a lift accelerated upwards at a certain rate, a spring balance indicates a weight to have a mass of 10kg. When the lift is accelerated downwards at twice the upward rate, the mass appears to be 7kg. Find the actual mass and the upward acceleration of the lift."

In short, I am stuck. I think this question involves simultaneus equations, but i can't get a set of equations that make sense. I've looked at the textbooks I have but they all concern themselves with the resistance forces or tensions in the strings.

A spring balance really measures force, not mass. It is marked with mass units assuming you will be using it in an inertial (non-accelerating) frame of reference. When it reads 10kg that really means the force it is measuring is 10kg(g) and when it reads 7kg, that means the force is 7kg(g)

Call the upward acceleration a and the downward acceleration -2a, taking positive upward in all cases.

F = ma = Force of spring balance (up) acting on m - weight
F = -2ma = Force of spring balance (down) acting on m - weight

Replace the words with the correct quantities and you are on your way.

thanks for the help but I am still not sure what I am doing here...

f=ma
f=(10)a
f=10a (1)

f=ma
f=(7)(-2a)
f=-14a (2)

that seems wrong.

You say "thanks for the help" but you don't seem to understand what was said! OlderDan just told you that the "10kg" and "7kg" reading on the scale is NOT mass- it is force- you should be substituting it for f, not m. m is what you are asked to find.
Also you don't have "g" in your formulas- the weight of mass m is mg. When the scale reads "10 kg" it is actually measuring a force of 10g Newtons.

f= ma so, in order to accelerate the mass m upwards at acceleration a, the elevator must apply force ma to the mass, through the scale. The scale is reading the weight of the mass, mg, plus the force ma: ma+ mg= m(a+g)= 10g
When the elevator is accelerating downwards, with acceleration -2a, and so the scale is reading -2ma+ mg= 7g Solve those two equations for m and a (g= 9.81 m/s2, of course).

## 1. What are the three laws of motion?

The three laws of motion, also known as Newton's laws of motion, are fundamental principles that describe the behavior of objects in motion. They are:
1. An object will remain at rest or in uniform motion in a straight line unless acted upon by an external force (Law of Inertia).
2. The force acting on an object is directly proportional to its mass and acceleration (F=ma).
3. For every action, there is an equal and opposite reaction.

## 2. How do the laws of motion apply to vertical acceleration?

The laws of motion apply to vertical acceleration in the same way as they do to any other type of motion. The first law states that an object at rest will remain at rest unless acted upon by a force, and an object in motion will continue to move in a straight line at a constant speed unless acted upon by a force. The second law states that the force acting on an object is directly proportional to its mass and acceleration. This means that the greater the mass of an object, the more force is needed to accelerate it vertically. The third law states that for every action, there is an equal and opposite reaction. This means that when an object is accelerated vertically, there is an equal and opposite force acting in the opposite direction.

## 3. How does gravity affect vertical acceleration?

Gravity plays a significant role in vertical acceleration. According to Newton's law of gravitation, any two objects with mass will attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. This means that the closer an object is to the center of the Earth, the stronger the force of gravity, and the greater the acceleration towards the Earth's surface. Therefore, gravity is a crucial factor in determining the vertical acceleration of an object.

## 4. How do mass and weight affect vertical acceleration?

Mass and weight are often used interchangeably, but they are not the same. Mass is a measure of the amount of matter an object contains, while weight is a measure of the force of gravity acting on an object. In terms of vertical acceleration, an object's mass will determine how much force is needed to accelerate it vertically, while weight will determine the magnitude of the acceleration. The greater the mass of an object, the more force is needed to accelerate it vertically, and the greater its weight, the greater the acceleration.

## 5. What is the formula for calculating vertical acceleration?

The formula for calculating vertical acceleration is a = F/m, where a is the acceleration in meters per second squared (m/s^2), F is the force in Newtons (N), and m is the mass of the object in kilograms (kg). This formula is derived from Newton's second law of motion, which states that the force acting on an object is directly proportional to its mass and acceleration. By rearranging the formula, we can also calculate force or mass when given the other two variables.

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