Two blocks are attached to opposite ends of a massless rope that goes over a massless, frictionless, stationary pulley. One of t

Answer: 592.37m

Explanation:

Person D is represented by the blue line.

The total displacement is calculated by subtracting the initial position from the final position. Starting at (0,0), the path consists of moving down two blocks, then right six blocks, followed by moving up four blocks, and finally left one block.

Here, I consider the positive direction of the x-axis to the right and the positive direction of the y-axis as upward.

Thus, the new coordinates will be, with B representing a block:

P =(6*B - 1*B, -2*B + 4*B) = (5*B, 2*B)

Given that B = 110m

P = (550m, 220m)

The displacement corresponds to the length of the vector, since the change from the initial position (0,0) to P is simply P:

P = √(550^2 + 220^2) = 592.37m

Answer:

1) Marner experiences a greater change in velocity

2) This happens because Chara has a greater mass compared to Marner, leading to a smaller change in velocity for Chara

Explanation:

Here are the details:

Mitch Marner's mass = 80 kg

Zdano Chara’s mass = 116 kg

Marner's speed prior to the collision = 10 m/s

According to the conservation of momentum, the sum of momentum before the collision equals the sum of momentum afterward:

m₁×u₁ + m₂×u₂ = m₁×v₁ + m₂×v₂

Where;

m₁ = Mitch Marner's mass = 80 kg

m₂ = Zdano Chara's mass = 116 kg

u₁ = Mitch Marner's initial velocity = 10 m/s

u₂ = Zdano Chara's initial velocity = 0 m/s

v₁ = Mitch Marner's final velocity

v₂ = Zdano Chara's final velocity

Assuming a direct collision, both players will have an identical instantaneous velocity just after impact, thus;

v₁ = v₂ = v

The equation can be expressed as;

m₁×u₁ + m₂×u₂ = (m₁ + m₂) × v₂

Substituting the numbers gives;

80 × 10 + 116 × 0 = (80 + 116) × v = 196 × v

Which simplifies to;

80 × 10 + 116 × 0 = 196 × v

800 = 196 × v

Thus, v = 800/196 = 100/49 =

This means the final instantaneous velocity for both Marner and Chara is

The change in velocity for Marner =

The change in velocity for Chara =

Therefore;

1) Marner's velocity changes more significantly

2) The reason being her mass relative to the total mass of both is smaller than Chara's mass relative to their total mass

This indicates that Marner's velocity alteration exceeds that of Chara due to Marner's lower mass.

The storm is at least 7 miles away since light travels faster than sound, allowing us to estimate the distance of a lightning strike based on the time taken for the subsequent thunder.

Answer:

Explanation:

Friction Force

Friction forces arise when items come into contact with each other or a rough surface, especially when there is an attempt to move one against the other. Friction operates in the reverse direction of the intended motion: pushing to the right results in a friction force directed left.

In this scenario, we have two blocks: a 400 kg block on the ground and a 100 kg block positioned atop, secured to a vertical wall via a string. When we attempt to push the bottom block, it will not move freely because two friction forces come into play: one from the surface and the other from the contact between the two blocks, denoted as Fr1 and Fr2. The second block, constrained by the wall, cannot simply slide along with the first one.

The provided figure displays the free body diagrams.

The equilibrium condition for the first mass is given as

The mass m1 is subjected to an applied force Fa, such that slipping with mass m2 just begins, indicating no overall movement (a=0). We can solve for Fa using:

The second mass experiences an attempt to move rightward due to the friction force Fr2 while the string maintains its position through tension T. The horizontal axis equation can be outlined as follows:

The friction forces are calculated as

It is important to note that N1 signifies the reaction force from the surface acting on mass m1, which corresponds to the cumulative mass of m1+m2.

Substituting into [1]

Upon simplifying

Finally, entering the numerical values will yield:

(a) 12.0 V

The capacitor remains connected to the 12.0 V source until fully charged. Taking into account the capacitor's capacity, , the total charge held at the conclusion of this process is

Upon disconnecting the battery, the charge on the capacitor stays the same. The capacitance, C, does not change either, as it solely relies on the capacitor's characteristics (area and distance between plates), which stay constant. Hence, according to the relationship

and since neither Q nor C vary, the voltage V also remains at 12.0 V.

(b) (i) 24.0 V

In this scenario, the distance between the plates is doubled. Let's recall the formula for the capacitance of a parallel-plate capacitor:

where:

is the permittivity of free space

is the relative permittivity of the capacitor's material

A is the area of the plates

d is the distance separating the plates

As noted, the plate distance is now doubled: d'=2d. This indicates that the capacitance is halved: . The updated voltage across the plates is given by

Since Q (the charge) remains constant (the capacitor is isolated, preventing charge flow), the new voltage turns out to be

This leads us to a new voltage of

(c) (ii) 3.0 V

The area for each capacitor plate is determined as:

where r indicates the radius of the plate. In this situation, the radius is doubled: r'=2r. Therefore, the new area becomes

While the distance between the plates remained unchanged (d); consequently, the new capacitance can be expressed as

Thus, the capacitance has quadrupled, leading to a new voltage of

which equates to