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17 days ago

A machine gear consists of 0.10 kg of iron and 0.16 kg of copper.

2 answers:

6 0

The answer is option (c). Explanation: The mass of iron is 0.10 kg, and copper is 0.16 kg. The temperature increase, ΔT, is 35°C. The specific heat capacity of iron is noted as 450 J/kg°C, whereas that of copper is 390 J/kg°C. The heat generated by iron (H1) is computed as H1 = mass of iron x specific heat of iron x ΔT, which results in H1 = 0.10 x 450 x 35 = 1575 J. The heat generated by copper (H2) is calculated as H2 = mass of copper x specific heat of copper x ΔT, where H2 = 0.16 x 390 x 35 = 2184 J. The total heat, H, equals H1 + H2, which gives H = 1575 + 2184 = 3759 J, and upon rounding off, H = 4000 J.

Yuliya22 [3.3K]17 days ago

5 0

b. Explanation: Given the mass specifics of the iron and copper gear, alongside their respective specific heats, we can calculate heat gain for both materials. The total heat generated can also be summarized.

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Dee is on a swing in the playground. the chains are 2.5 m long, and the tension in each chain is 450 n when dee is 55 cm above t

kicyunya [3294]

Referencing the diagram below, we can deduce from the geometry that x = 2.5 - 0.55 = 1.95 m, leading to cos θ = 1.95/2.5 = 0.78. Therefore, θ = cos⁻¹ 0.78 = 38.74°. According to the free body diagram, the tension in the chain measures 450 N. Here, F denotes the centripetal force and W signifies Dee's weight. The tension's components are as follows: Horizontal component = 450 sin(38.74°) = 281.6 N, directed to the left, and Vertical component = 450 cos(38.74°) = 351.0 N, directed upward. Answers: Horizontal: 281.6, directed left. Vertical: 351.0 N, directed upward.

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19 days ago

A 20.00-kg lead sphere is hanging from a hook by a thin wire 2.80 m long and is free to swing in a complete circle. Suddenly it

Keith_Richards [3271]

Objects in vertical motion are an illustration of non-uniform motion. At the peak of the circle, centripetal force is balanced by the object's weight. Therefore, the minimum speed required at this top point is given by v = $\sqrt{rg}$ = $\sqrt{2.80 \times 9.8}$ = 5.23 m/s. As the sphere descends from the top to the bottom of the circle, according to the law of conservation of energy, potential energy can be expressed as

$P.E_{highest} = mgh$

, where h signifies the diameter of the circle (2r). Hence, the expression will be written as $P.E_{highest} = mg(2r)$

where u is the velocity at the lowest point. Consequently, the modified equation is

= $\sqrt{v^{2} + 4gr}$

= $\sqrt{(5.23)^{2} + (4 \times 9.8 \times 2.80)}$

= 11.71 m/s. The collision of the dart with the bullet is an inelastic one. According to the conservation of momentum: v = $\frac{(m_{1} + m_{2})u}{m_{2}}$

= $\frac{(20 + 5) \times 11.71}{5}$

= $\frac{292.75}{5}$

= 58.55 m/s. Thus, the dart's minimum initial speed for the combined system to complete a circular loop post-collision is 58.55 m/s.

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17 days ago

A model of a spring/mass system is 4x'' + e−0.1tx = 0. By inspection of the differential equation only, discuss the behavior of

Keith_Richards [3271]

Displacement stabilizes over time. It is known that exponentials raised to infinity approach zero, hence the system model will yield as time approaches infinity, resulting in 4x'' + e−0.1tx = 0. As time approaches infinity, we deduce that 4x'' equals zero. Consequently, upon integrating, we derive 4x' = c, and further integration leads to the conclusion 4x = cx + d.

4 0

17 days ago

An electron and a proton, starting from rest, are accelerated through an electric potential difference of the same magnitude. in

ValentinkaMS [3465]

Since the absolute values of the charges are identical, the changes in potential energy remain equivalent. Consequently, the changes in kinetic energy will also match. We have:

1 = Ke/Kp = m_e * v_e^2 / m_p * v_p^2, which simplifies to:

v_e/v_p = sqrt(m_p/m_e),

indicating that the velocity of the electron is sqrt(m_p/m_e) times greater than that of the proton.

4 0

1 month ago

A basketball center holds a basketball straight out, 2.0 m above the floor, and releases it. It bounces off the floor and rises

Softa [3030]

Answer:

a) The ball's velocity just prior to hitting the ground measures -6.3 m/s

b) The ball's velocity right after bouncing off the ground registers at 3.1 m/s

c) The average acceleration's magnitude is 470 m/s², and its direction is upward, forming a 90º angle with the ground.

Explanation:

To begin, let’s assess the time it takes for the ball to reach the floor:

The equation outlining the ball's position is:

y = y0 + v0 * t + 1/2 g * t²

Where:

y = position at given time t

y0 = initial position

v0 = initial velocity

t = time

g = acceleration triggered by gravity

We establish the ground as the reference origin.

a) Since the ball is released rather than thrown, the initial velocity v0 is 0. The direction of acceleration is downward, directed towards the origin; thus, “g” is treated as negative. When the ball contacts the ground, its position will be 0. Therefore:

0 = 2.0 m + 0 m/s *t - 1/2 * 9.8 m/s² * t²

-2.0 m = -4.9 m/s² * t²

t² = -2.0 m / - 4.9 m/s²

t = 0.64 s

The motion equation for a falling body is:

v = v0 + g * t where "v" denotes the velocity

Since v0= 0:

v = g * t = -9.8 m/s² * 0.64 s = -6.3 m/s

b) The pebble's speed reaches 0 during its maximum height. To find the time taken for the pebble to achieve that height, we can use the velocity equation and then substitute that time in the position equation to derive the initial velocity:

v = v0 + g * t

0 = v0 + g * t

-v0/g = t

Replacing t in the position equation, knowing the maximum height is 1.5 m:

y = y0 + v0 * t + 1/2* g * t² y = 1.5 m y0 = 0 m t = -v0/g

1.5 m = v0 * (-v0/g) + 1/2 * g (-v0/g)²

1.5 m = - v0²/g - 1/2 * v0²/g

1.5 m = -3/2 v0²/g

1.5 m * (-2/3) * g = v0²

1.5 m * (-2/3) * (-9.8 m/s²) = v0²

v0 = 3.1 m/s

c) The average acceleration can be determined by:

a = final velocity - initial velocity / time

a = 3.1 m/s - (-6.3 m/s) / 0.02 s = 470 m/s²

The direction of the acceleration is upward, perpendicular to the ground.

The vector average acceleration will be:

a = (0, 470 m/s²) or (470 m/s² * cos 90º, 470 m/s² * sin 90º)

4 0

22 days ago