If a constant force of 800N produces an acceleration of 5 m/s² in a body, what is its mass? If the body starts from rest, how much distance will it travel in 10 s?
Understand the Problem
The question is asking us to find the mass of a body given a constant force and the acceleration produced by it. It also asks for the distance the body will travel in 10 seconds if it starts from rest. To solve this, we will use Newton's second law to find the mass and the equations of motion to find the distance traveled.
Answer
The mass of the body is \( 160 \, \text{kg} \) and the distance it will travel in 10 seconds is \( 250 \, \text{m} \).
Answer for screen readers
The mass of the body is ( 160 , \text{kg} ) and the distance it will travel in 10 seconds is ( 250 , \text{m} ).
Steps to Solve
- Calculate the Mass of the Body
Using Newton's second law of motion, the formula is given by:
$$ F = m \times a $$
Where:
- ( F ) is the force (800 N)
- ( m ) is the mass (unknown)
- ( a ) is the acceleration (5 m/s²)
Rearranging the formula to solve for mass ( m ):
$$ m = \frac{F}{a} $$
Substituting the known values:
$$ m = \frac{800 , \text{N}}{5 , \text{m/s}^2} = 160 , \text{kg} $$
- Calculate the Distance Traveled in 10 Seconds
To find the distance traveled ( d ) under constant acceleration, we can use the equation of motion:
$$ d = v_0 t + \frac{1}{2} a t^2 $$
Where:
- ( v_0 ) is the initial velocity (0 m/s, since it starts from rest)
- ( a ) is the acceleration (5 m/s²)
- ( t ) is the time (10 s)
Since ( v_0 = 0 ):
$$ d = 0 + \frac{1}{2} \times 5 , \text{m/s}^2 \times (10 , \text{s})^2 $$
Now, calculate the distance:
$$ d = \frac{1}{2} \times 5 \times 100 = 250 , \text{m} $$
The mass of the body is ( 160 , \text{kg} ) and the distance it will travel in 10 seconds is ( 250 , \text{m} ).
More Information
This problem illustrates how to connect the concepts of force, mass, and acceleration through Newton's second law. The calculation of distance under uniform acceleration applies basic kinematic equations, which are foundational in physics.
Tips
- Forgetting to convert units if necessary, such as using different units for force and mass. Always check the consistency of units.
- Misapplying the equations; remember that if the object starts from rest, the initial velocity is zero.
- Neglecting to square the time when using the kinematic equations, which can lead to incorrect distance calculations.
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