# Determine is box of unknown mass is sliding down a ramp?

• Jojo96
In summary, the conversation discusses a problem involving a box of unknown mass on a loading ramp with an angle of 16 degrees. The coefficient of static friction is 0.30 and kinetic friction is 0.25. The question is whether the box will start sliding down the ramp and if it does, what will be the acceleration of the box. The solution involves calculating the forces in the x-direction and using the equation ∑F=ma to determine if the weight of the box is enough to overcome static friction.
Jojo96

## Homework Statement

A box of textbooks at unknown mass rests on a loading ramp that makes an angle α = 16o with the horizontal. The coefficient of static friction is 0.30, and kinetic friction is 0.25. Then the box is released. (a) Will it start sliding down the ramp? (a) Find the normal force on the box (b) If it slides down then find the acceleration of the box

2. Relevant
F=ma
ƒ=µn

## The Attempt at a Solution

Forces in x-direction:
w-ƒstatic=0
w=ƒstatic
mgsin(16)=µn
y: n-w=0
n=w
n=mgcos(16)
------
mgsin(16)=µmgcos(16)
sin(16)=µcos(16)
sin(16)/cos(16)=µ
But already know µ so this doesn't help me...
[/B]

By assuming ##\sum F_x=0## you're stating that the block isn't moving in the x direction. Try using ##\sum F_x=ma_x##

Jojo96 said:
3. The Attempt at a Solution
Forces in x-direction:
w-ƒstatic=0
w=ƒstatic
mgsin(16)=µn
y: n-w=0
n=w
n=mgcos(16)
------
mgsin(16)=µmgcos(16)
sin(16)=µcos(16)
sin(16)/cos(16)=µ
But already know µ so this doesn't help me...

with the ramp at your angle theta - if you calculate the force driving the box then perhaps it will come out less than the frictional force opposing the tendency to slide down- as it will be mu. M.g .cos (angle)

The only force that is driving it down is the weight. Nothing is pulling the box. Also, what would I use for acceleration in the x direction for F=ma?

Jojo96 said:
The only force that is driving it down is the weight. Nothing is pulling the box. Also, what would I use for acceleration in the x direction for F=ma?
Component of weight along the slope is pulling the box down. Check if it is sufficient to overcome static friction.

Jojo96 said:
The only force that is driving it down is the weight. Nothing is pulling the box. Also, what would I use for acceleration in the x direction for F=ma?

along the ramp the force acting downward will be component of Mg - i.e. Mg sin(16)- but your body can not move with this pull along the ramp as frictional force is larger - if you increase the angle of ramp then only it can move at an angle Theta such that Mgsin(theta) exceeds
(Coeff. of friction XMg Cos(theta)) which is opposing the motion acting along the ramp in upward direction.

## 1. How do you determine the mass of an unknown box sliding down a ramp?

In order to determine the mass of an unknown box sliding down a ramp, you will need to measure the acceleration of the box as it slides down the ramp. This can be done using a device called an accelerometer, which measures acceleration in meters per second squared (m/s^2). Once you have the acceleration, you can use the formula F=ma (force = mass x acceleration) to solve for the mass of the box.

## 2. What factors can affect the acceleration of a box sliding down a ramp?

There are several factors that can affect the acceleration of a box sliding down a ramp. These include the angle of the ramp, the friction between the box and the ramp, the mass of the box, and the force applied to the box (if any). Other factors such as air resistance and the surface of the ramp can also have an impact on the acceleration.

## 3. How can you ensure accurate measurements when determining the mass of a box sliding down a ramp?

To ensure accurate measurements, it is important to use precise tools and equipment, such as an accurate accelerometer and a level ramp. It is also important to repeat the experiment multiple times and take an average of the results to minimize any errors. Additionally, the experiment should be conducted in a controlled environment to eliminate any external factors that could affect the results.

## 4. What is the significance of determining the mass of a box sliding down a ramp?

Determining the mass of a box sliding down a ramp is significant because it allows us to understand the relationship between mass, force, and acceleration. This is an important concept in physics and can be applied to various real-life situations, such as designing efficient ramps for moving heavy objects or understanding the motion of objects in freefall.

## 5. Can the same method be used to determine the mass of any object sliding down a ramp?

Yes, the same method of measuring acceleration and using the formula F=ma can be used to determine the mass of any object sliding down a ramp. However, the accuracy of the measurements may vary depending on the shape, size, and weight of the object, as well as the surface and angle of the ramp. It is important to consider these factors when conducting the experiment and interpreting the results.

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