To develop this problem it is necessary to apply the concepts related to the Cross Product of two vectors as well as to obtain the angle through the magnitude of the angles.

The vector product between the Force and the radius allows us to obtain the torque, in this way,

$\tau = \vec{F} \times \vec{r}$

$\tau = (8i+6j)\times(-3i+4j)$

$\tau = (8*4)(i\times j)+(6*-3)(j\times i)$

$\tau = 32k +18k$

$\tau = 50 k$

Therefore the torque on the particle about the origen is 50k

PART B) To find the angle between two vectors we apply the definition of the dot product based on the vector quantities, that is,

$cos\theta = \frac{r\cdot F}{|\vec{r}|*|\vec{F}|}$

$cos\theta = \frac{(8*-3)+(4*3)}{\sqrt{(-3)^2+4^2}*\sqrt{8^2+6^2}}$

$cos\theta = -0.24$

$\theta = cos^{-1} (-0.24)$

$\theta = 103.88\°$

Therefore the angle between the ratio and the force is 103.88°

5 0

3 years ago

Which is not expecting acceleration?

Kamila [148]

1. Answer: A skydiver whose air resistance is equal to that of her weight.

A skydiver free falls under gravity but her rate of fall slows down due to drag -air resistance. when this air resistance becomes equal to her weight, the two get balanced and the body does not accelerate or decelerates.

2. Answer: Gravity

Contact forces are those which act when there is physical contact between two bodies. For example: normal force, tension and spring force.

Non-contact forces act between two bodies even when they are at a distance apart. For example: gravity, electric force, magnetic force etc.

3. Answer: The tendency of an object's motion to remain the same.

Inertia is a property of matter by virtue of which it tends to remain in its state of motion or rest. It does depend on mass of the object, more the mass, more is inertia. For example, cycle can be easily moved but we need real push hard for a car to move.

4. Answer: 254 N

The man pushes the box with 310 N force at an angle of 55 degrees to the horizontal.

we can write this in terms of horizontal ( $F cos \theta$ )and vertical component ( $F sin\theta$ ).