How much work is needed to move an object 20 meters with 40 newtons of force?

In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their component

JulijaS [17]

Answer:

The calculated vectors are:

$\vec{A}-\vec{B}=(3,-5,-4)$

$\vec{B}-\vec{C}=(-5,4,0)$

$-\vec{A}+\vec{B}-\vec{C}=(-6,4,3)$

$3\vec{A}-2\vec{C}=(-3,-2,-11)$

Explanation:

To operate with vectors, you sum or rest component to component. To multiply scalars with vectors, you distribute the scalar with each component of the vector. These are the following rules you must apply in these cases:

$\vec{V}+\vec{W}=(V_1,V_2,V_3)+(W_1,W_2,W_3)=(V_1+W_1,V_2+W_2,V_3+W_3)$ (1)

$\vec{V}-\vec{W}=(V_1,V_2,V_3)-(W_1,W_2,W_3)=(V_1-W_1,V_2-W_2,V_3-W_3)$ (2)

$\alpha\cdot\vec{V}=\alpha\cdot(V_1,V_2,V_3)=(\alpha\cdot V_1,\alpha\cdot V_2,\alpha\cdot V_3)$ (3)

The operations in these cases are:

$\vec{A}-\vec{B}=(1,0, -3)-(-2,5,1)=(3,-5,-4)$

$\vec{B}-\vec{C}=(-2,5,1)-(3,1,1)=(-5,4,0)$

$-\vec{A}+\vec{B}-\vec{C}=-(1,0, -3)+(-2,5,1)-(3,1,1)=(-6,4,3)$

$3\vec{A}-2\vec{C}=3(1,0, -3)-2(3,1,1)=(3,0, -9)-(6,2,2)=(-3,-2,-11)$

3 0

3 years ago

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A box of mass m = 1.80 kg is dropped from rest onto a massless, vertical spring with spring constant k = 2.00 ✕ 102 N/m that is

Rudik [331]

Answer:

spring compressed is 0.724 m

Explanation:

given data

mass = 1.80 kg

spring constant k = 2 × 10² N/m

initial height = 2.25 m

solution

we know from conservation of energy is

mg(h+x) = 0.5 × k × x² ...................1

here x is compression in spring

so put here value in equation 1 we get

1.8 × 9.8 × (2.25+x) = 0.5 × 2× 10² × x²

solve it we get

x = 0.724344

so spring compressed is 0.724 m

3 0

4 years ago

ou are walking down a straight path in a park and notice there is another person walking some distance ahead of you. The distanc

alexgriva [62]

Answer:

The value is $d = 31.45 \ m$

Explanation:

Generally the relative speed at which you are moving with respect to the person ahead of you is mathematically represented as

$v_r = v_s - v_c$

substituting 1.05 m/s for $v_c$ and 2.75 m/s for $v_s$

So

$v_r = 2.75 - 1.05$

=> $v_r = 1.7 \ m/s$

Generally the distance by which the person is ahead of you is mathematically represented as

$d = v_r * t$

substituting 18.5 s for $t$

$d = 1.7 * 18.5$

=> $d = 31.45 \ m$

4 0

3 years ago

Two students, standing on skateboards, are initially at rest, when they give each other a shove! After the shove, one student (7

Elden [556K]

Answer:

The other student (59kg) moves right at 7.44 m/s

Explanation:

Given;

mass of the first student, m₁ = 77kg

mass of the second student, m₂ = 59kg

initial velocity of the first student, u₁ = 0

initial velocity of the second student, u₂ = 0

final velocity of the first student, v₁ = 5.7 m/s left

final velocity of the second student, v₂ = ? right

Apply the principle of conservation of linear momentum;

Total momentum before collision = Total momentum after collision

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(77 x 0) + (59 x 0) = (-77 x 5.7) + (59 x v₂)

0 = - 438.9 + 59v₂

59v₂ = 438.9

v₂ = 438.9 / 59

v₂ = 7.44 m/s to the right

Therefore, the other student (59kg) moves right at 7.44 m/s

6 0

3 years ago

Which of the circuit offers greater resistance to the flow of current 1A or 2A ?

Dafna1 [17]

1 A offers greater resistance

7 0

3 years ago

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