We read your photo as:

A block is acted upon by forces of 430N, 100N, 450N, and 800N. Determine the net force on the block.

Physics

ScanSolve AI Answer

Answer

1926.76 N1926.76 \, \text{N}

80.44∘ below the positive horizontal axis80.44^\circ \text{ below the positive horizontal axis}

Step-by-step solution

4 steps
  1. Calculate the net horizontal force.

    We'll consider forces to the right as positive and forces to the left as negative.

    Fnet,x=750 N−430 NF_{net,x} = 750 \, \text{N} - 430 \, \text{N} Fnet,x=320 N (to the right)F_{net,x} = 320 \, \text{N} \text{ (to the right)}
  2. Calculate the net vertical force.

    We'll consider forces downwards as negative.

    Fnet,y=−100 N−800 N−1000 NF_{net,y} = -100 \, \text{N} - 800 \, \text{N} - 1000 \, \text{N} Fnet,y=−1900 N (downwards)F_{net,y} = -1900 \, \text{N} \text{ (downwards)}
  3. Calculate the magnitude of the resultant net force.

    The magnitude of the net force is found using the Pythagorean theorem:

    Fnet=Fnet,x2+Fnet,y2F_{net} = \sqrt{F_{net,x}^2 + F_{net,y}^2} Fnet=(320 N)2+(−1900 N)2F_{net} = \sqrt{(320 \, \text{N})^2 + (-1900 \, \text{N})^2} Fnet=102400 N2+3610000 N2F_{net} = \sqrt{102400 \, \text{N}^2 + 3610000 \, \text{N}^2} Fnet=3712400 N2F_{net} = \sqrt{3712400 \, \text{N}^2} Fnet≈1926.76 NF_{net} \approx 1926.76 \, \text{N}
  4. Calculate the direction of the resultant net force.

    The angle θ\theta with respect to the positive x-axis (horizontal to the right) is given by:

    θ=arctan⁡(Fnet,yFnet,x)\theta = \arctan\left(\frac{F_{net,y}}{F_{net,x}}\right) θ=arctan⁡(−1900 N320 N)\theta = \arctan\left(\frac{-1900 \, \text{N}}{320 \, \text{N}}\right) θ=arctan⁡(−5.9375)\theta = \arctan(-5.9375) θ≈−80.44∘\theta \approx -80.44^\circ

    This means the force is 80.44∘80.44^\circ below the horizontal, in the fourth quadrant.

    The magnitude of the net force is 1926.76 N\boxed{1926.76 \, \text{N}} at an angle of 80.44∘ below the positive horizontal axis\boxed{80.44^\circ \text{ below the positive horizontal axis}}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp