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3 years ago

Use this free body diagram to help you find the magnitude of the force needed to keep this block in static equilibrium.

Physics

1 answer:

Bingel [31]3 years ago

8 0

Split F₁ into its horizontal and vertical components:

F₁ = F₁ cos(θ) i + F₁ sin(θ) j

(boldface = vector; regular font = magnitude)

By Newton's second law, if the object is in equilibrium, then

• the net horizontal force on the block is

∑ F = F₁ cos(θ) - F₃ = 0 → F₁ cos(θ) = 70 N

• the net vertical force is

∑ F = F₁ sin(θ) + F₂ - W = 0 → F₁ sin(θ) = 65 N

Recall that cos²(θ) + sin²(θ) = 1 for any θ, so we have

(F₁ cos(θ))² + (F₁ sin(θ))² = (70 N)² + (65 N)²

F₁² = 9125 N²

F₁ = √(9125 N²) ≈ 95.5 N

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An amateur player is about to throw a dart with an initial velocity of 15 meters/second onto a dartboard that is at a distance o

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B. 0.16 m

Explanation:

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Since the dart is thrown horizontally, the initial vertical velocity is zero:

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3 years ago

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3 years ago

Read 2 more answers

How far from Earth must a space probe be along a line toward the Sun so that the Sun's gravitational pull on the probe balances

Tatiana [17]

Answer:

258774.9441 m

Explanation:

x = Distance of probe from Earth

y = Distance of probe from Sun

Distance between Earth and Sun = $x+y=149.6\times 10^6\ m$

G = Gravitational constant

$M_s$ = Mass of Sun = $1.989\times 10^{30}$

$M_e$ = Mass of Earth = $5.972\times 10^{24}\ kg$

According to the question

$\frac{GM_sm}{x^2}=\frac{GM_em}{y^2}\\\Rightarrow \frac{M_s}{x^2}=\frac{M_e}{y^2}\\\Rightarrow x=\sqrt{\frac{M_s\times y^2}{M_e}}\\\Rightarrow x=\sqrt{\frac{1.989\times 10^{30}\times y^2}{5.972\times 10^{24}}}\\\Rightarrow x=577.10852y$

$x+y=149.6\times 10^6\\\Rightarrow 577.10852y+y=149.6\times 10^6\\\Rightarrow 578.10852y=149.6\times 10^6\\\Rightarrow y=\frac{149.6\times 10^6}{578.10852}\\\Rightarrow y=258774.9441\ m$

The probe should be 258774.9441 m from Earth

7 0

3 years ago

A golden retriever is sitting in a park when it sees a squirrel. The dog starts running, exerting a constant horizontal force of

oksano4ka [1.4K]

Answer:

284.8 kgm/s

Explanation:

Impulse: This can be defined as the product of force and time of a body. The S.I unit of impulse is N.s mathematically.

Impulse = Force × time

Change in momentum: This is the product of the mass of a body and its change in velocity. The unit of change in momentum is kgm/s.

Mathematically,

momentum = mass×change in velocity

Deduction from newton's second law of motion,

Impulse = change in momentum

Therefore,

Change in Momentum = Force×time

ΔM = F×t................. Equation 1

Where F = force = 89 N, t =time = 3.2 s.

Substitute into equation 1

ΔM = 89×3.2

ΔM = 284.8 kgm/s

Thus the change in momentum = 284.8 kgm/s

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3 years ago