In mathematical form, torque or moment of force is given by _____. a) r x F b) F x r c) F.r d) r.F If a constant force of 800N produces an acceleration of 5 m/s² in a body, what is... In mathematical form, torque or moment of force is given by _____. a) r x F b) F x r c) F.r d) r.F 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 10s?
Understand the Problem
The question is asking about two separate physics concepts: the mathematical expression of torque and a problem involving force, acceleration, mass, and distance traveled. For the first part, it requires identifying the correct mathematical representation of torque from the options given. The second part involves applying the equations of motion to determine how far a body travels under a given force and acceleration over a specified time.
Answer
The torque is given by $\tau = r \times F$. The mass is $160 \, \text{kg}$, and the distance traveled is $250 \, \text{m}$.
Answer for screen readers
The correct mathematical expression for torque is $\tau = r \times F$. The mass of the body is $160 , \text{kg}$, and the distance traveled is $250 , \text{m}$.
Steps to Solve
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Identify the mathematical expression for torque
The torque or moment of force $\tau$ is calculated as the cross product of the radius vector $r$ and the force vector $F$. Therefore, the correct expression is:
$$ \tau = r \times F $$
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Find the mass of the body
Using Newton's second law of motion, $F = ma$, we can rearrange to find the mass $m$:
$$ m = \frac{F}{a} $$
Plugging in the values:
- Force, $F = 800 , \text{N}$
- Acceleration, $a = 5 , \text{m/s}^2$
$$ m = \frac{800}{5} = 160 , \text{kg} $$
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Calculate the distance traveled
Using the formula for distance in uniformly accelerated motion:
$$ s = ut + \frac{1}{2} a t^2 $$
Given that $u = 0$ (initial velocity), $a = 5 , \text{m/s}^2$, and $t = 10 , \text{s}$:
$$ s = 0 \cdot 10 + \frac{1}{2} \cdot 5 \cdot (10^2) = \frac{1}{2} \cdot 5 \cdot 100 = 250 , \text{m} $$
The correct mathematical expression for torque is $\tau = r \times F$. The mass of the body is $160 , \text{kg}$, and the distance traveled is $250 , \text{m}$.
More Information
Torque represents the rotational equivalent of linear force. A force causing a given acceleration provides means to calculate mass. The distance traveled is determined under constant acceleration, a fundamental concept in physics.
Tips
- Confusing torque terms; remember that torque uses the cross product ($\times$).
- Not accounting for initial velocity when calculating distance; ensure initial velocity is set correctly (0 in this case).
- Miscalculating mass by not using the correct relationship between force, mass, and acceleration.
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