# How does friction affect the acceleration of a box being pulled by a rope?

• David Donald
In summary, a 25 kg box is pulled by a 40 N force of tension at a 30 degree angle with the horizontal. The acceleration of the box is 1.38 m/s^2 and the equation for finding acceleration in the presence of a friction force of 3.0 N is (∑Fx = F - Ff = ma = (40N(cos(30) - 3N)/(25kg) = 1.26 m/s^2). If a small box of 5kg with a frictional force of 2.0 N is placed against the right side of the box, the big box would move with an acceleration of 0.988 m/s^2. The vertical component of
David Donald

## Homework Statement

A box of m= 25 kg is pulled by a rope with a force of tension, F = 40 N inclined at an angle of 30o with the horizontal, there is no friction between the box and the ground.
b) Determine
the acceleration of the box.
c) Write the equation to find the acceleration
of the box in presence of a friction force of 3.0
N.
d) If a small box of 5kg with a frictional force of 2.0 N is placed against the right side of the box. Would the big box move? If so what would its acceleration be?

Please check my work and let me know if I've made any mistakes..

## The Attempt at a Solution

B) F = ma

(40N*Cos(30))/(25kg) = acceleration = 1.38 m/s^2

C)
∑Fx = F - Ff = ma
= (40N(cos(30) - 3N)/(25kg) = 1.26 m/s^2

d) So for this one I used the same equation I came up with in C) except mass is now 30kg because it's 25 kg box + the 5 kg box and the friction force is now 5 N

∑Fx = F - Ff = ma
= (40N(cos(30) - 5N)/(30kg) = 0.988 m/s^2

Now I don't know how to answer the word part... I would say yes it would move because their is a positive acceleration

B: did you check the vertical component ... does the box stay on the ground?
D: it seems to want you to say if the box would move without first calculating the acceleration ... i.e. compare the friction forces to the rope force.

I'm sorry I don't quite understand how could i tell by the vertical component whether it would stay on the ground or not?

The vertical component would be how hard the rope pulls the box upwards ... is that hard enough to pull the box off the ground?

## 1. What is the definition of force on a box?

Force on a box is the amount of external energy or influence that is applied to a box, causing it to accelerate or change its state of motion.

## 2. How is force on a box calculated?

Force on a box is calculated by multiplying the mass of the box by its acceleration. This is known as Newton's Second Law of Motion (F=ma).

## 3. What factors can affect the force on a box?

The force on a box can be affected by the mass of the box, the acceleration of the box, and the direction of the force. Other factors such as friction and air resistance may also play a role.

## 4. Can the force on a box be negative?

Yes, the force on a box can be negative if the direction of the force is opposite to the direction of motion. This is known as a negative or opposing force.

## 5. How can force on a box be measured?

Force on a box can be measured using a force meter or a spring scale. The force meter measures the amount of force being applied to the box, while the spring scale measures the amount of stretch in a spring when attached to the box.

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