If a woman weighs 125 lb, her mass expressed in kilograms is x kg, where x is

1. τbiceps = +(Positive) 2. τforearm = -(Negative) 3. τball = -(Negative) Explanation: The attached figure illustrates the following: 1. For the biceps, τbiceps indicates that torque is calculated as Torque = r x F, where r and F are vectors. Here, r corresponds to the vector from the elbow to the biceps. In the figure, the force from the biceps is directed upwards. Applying the right-hand rule from r to F results in counterclockwise torque, which is considered positive (+). 2. The torque related to the weight of the forearm, τforearm, uses the same torque formula, with r being the vector from the elbow to the forearm. The weight acts downward, causing a clockwise torque that is negative (-). 3. Similarly, for the weight of the ball, τball, the downward force from the ball's weight generates a clockwise torque, which also registers as negative (-).

The work performed to elevate the box equals 515.03 J.

Answer:

According to the guideline for kilometers, every three seconds between a lightning strike and the subsequent thunder indicates the distance to the flash in kilometers.

Explanation:

To calculate the speed of sound in meters per second, we need to utilize certain conversion factors. One mile corresponds to 5 seconds after witnessing the lightning. Furthermore, 1 mile comprises 5280 feet, and 1 foot is equivalent to 0.3048 meters. This information is sufficient to solve the issue. The conversion ratios can be set up like this:

Observe how the ratios are organized such that the units cancel out during calculations. One ratio has miles in the numerator while the other has them in the denominator, leading to cancellation. The same applies to the feet.

The question requires us to provide the answer to one significant figure, resulting in the speed of sound rounding to 300m/s.

For the second part, we will again utilize conversions. This time we will set our ratios in reverse and realize that there are 1000 meters in 1 kilometer, leading us to:

This signifies that for every 3.11 seconds, the distance to the lightning strike is 1 kilometer. Since this is a fabric of general knowledge, we round to the nearest whole number for simplicity, establishing the guideline:

According to the rule for kilometers, every three seconds between a lightning flash and the following thunder gives the distance to the flash in kilometers.

Refer to the diagram below.

Ignoring air resistance, use gravitational acceleration g = 9.8 m/s².

The pole vaulter drops with an initial vertical speed u = 0.
At impact with the pad, velocity v satisfies:
v² = 2 × (9.8 m/s²) × (4.2 m) = 82.32 (m/s)²
v = 9.037 m/s

As the pad compresses by 0.5 m to bring the vaulter to rest,
let the average acceleration (deceleration) be a m/s². Then:
0 = (9.037 m/s)² + 2 × a × 0.5 m
Solving for a gives:
a = - 82.32 / (2 × 0.5) = -82 m/s²

Thus, the deceleration magnitude is 82 m/s².

Answer:

a)  τ = i ^ (y - z ) + j ^ (z Fₓ - x ) + k ^ (x - y Fₓ)

b) τ = (-0.189i ^ -5.6 j ^ + 33.978k ^) N m

c) α = (-7.8 10⁻⁴ i ^ - 2.3 10⁻² j ^ + 1.4 10⁻¹ k ^) rad / s²

Explanation:

a) The torque can be expressed as

        τ = r x F

To tackle this equation, using the determinant approach is the most straightforward method

         

The resulting expression is

      τ = i ^ (y - z ) + j ^ (z Fₓ - x ) + k ^ (x - y Fₓ)

b) Now let's compute

     τ = i ^ (0.075 1.4 -0.035 8.4) + j ^ (0.035 2.8 - 4.07 1.4) + k ^ (4.07 8.4 - 0.075 2.8)

     τ = i ^ (- 0.189) + j ^ (-5.6) + k ^ (33,978)

     τ = (-0.189i ^ -5.6 j ^ + 33.978k ^) N m

c) To find angular acceleration, we use

       τ = I α

       α = τ / I

The moment of inertia being a scalar means that only the magnitude of each component changes, orientation remains constant.

           

     α = (-0.189i^  -5.6 j^  + 33.978k^) / 241

     α = (-7.8 10⁻⁴ i ^ - 2.3 10⁻² j ^ + 1.4 10⁻¹ k ^) rad / s²