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netineya [11]
3 years ago
7

An object of mass m has these three forces acting on it (there is no normal force, "no surface"). F1 = 5 N, F2 = 8 N, and F3 = 5

N. When answering the questions below, assume the x-direction is to the right, and the y-direction is straight upwards.
a) What is the net force in component form, in terms of F1, F2, F3, and the unit vectors i and j
b) What is the magnitude of the net force, in newtons?
c) What is the angle θ, in degrees, of the net force, measured from the +x-axis? Enter an angle between -180° and 180°.
d) What is the magnitude, |a| of the acceleration, in meters per square second, if the block has a mass of 6.9 kg?

Physics
1 answer:
DIA [1.3K]3 years ago
4 0

The figure is missing: find it in attachment.

a) (3i - 5j) N

First of all, we have to write each force as a vector with a direction:

- Force F1 points downward, so along the negative y-direction, so we can write it as

F_1 = -5 j

- Force F2 points to the right, so along the positive x-direction, so we can write it as

F_2 = +8 i

- Force F3 points to the left, so along the negative x-direction, so we can write it as

F_3 = -5 i

Now we can write the net force, by adding the three vectors and separating the x-component from the y-component:

F=F_1+F_2+F_3 = -5j+8i-5i = (8-5)i+(-5)j=(3i-5j)N

b) 5.8 N

The magnitude of the net force can be calculated by applying Pythagorean's theorem on the components of the net force:

F=\sqrt{F_x^2+F_y^2}

where

F_x = 3 N is the x-component

F_y = -5 N is the y-component

Substituting into the equation,

F=\sqrt{(3)^2+(-5)^2}=5.8 N

c) -59.0^{\circ}

The angle of the net force, measured with respect to the positive x-axis (counterclockwise), can be calculated by using the formula

\theta=tan^{-1} (\frac{F_y}{F_x})

where

F_x = 3 N is the x-component

F_y = -5 N is the y-component

Substituting into the equation, we find

\theta = tan^{-1} (\frac{-5}{3})=-59.0^{\circ}

d) 0.84 m/s^2

The acceleration can be found by using Newton's second law:

F=ma

where

F is the net force on an object

m is its mass

a is the acceleration

For the object in the problem, we know

F = 5.8 N

m = 6.9 kg

Solving the equation for a, we find the magnitude of the acceleration:

a=\frac{F}{m}=\frac{5.8}{6.9}=0.84 m/s^2

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N  = 6.67 N

Explanation:

The frictional or frictional force is a force that arises from the contact of two bodies and opposes movement.

The friction is due to imperfections and roughness, mainly microscopic, that exist on the surfaces of the bodies. Upon contact, these roughnesses engage with each other making movement difficult. To minimize the effect of friction, either the surfaces are polished or lubricated, since the oil fills the imperfections, preventing them from snagging.

As the frictional force depends on the materials and the force exerted on one another, its magnitude is obtained by the following expression:

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We replace data in the formula (1)

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N  = 0.2 / 0.03

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