You have devised an experiment to measure the kinetic coefficient of friction between a ramp and block. You place the block on the ramp at an angle high enough that it starts sliding. You measure the time it takes to fall down a known distance. The time it takes to fall down the ramp starting from a standstill is 0.5 sec, ???? = 1 kg, θ = 45o, and the distance it falls, L, is 0.5 m. What is µk? (8 pts)

Answers

Answer 1

Answer:

Answer:

μ = 0.423

Explanation:

To solve this exercise we must use Newton's second law and kinematics together, let's start using expressions of kinematics to find the acceleration of the body

Let's fix a reference system where the x axis is parallel to the inclined plane, but the acceleration is only on this axis

x = v₀ t + ½ a t²

The body starts from rest so its initial speed is zero

a = 2 x / t²

a = 2 0.5 /0.5²

a = 4 m / s²

Taking the acceleration of the body, we use Newton's second law, we take the direction up the plane as positive

X axis

fr - Wₓ = m a (1)

Y Axis

N- $W_(y)$ = 0

N = W_{y}

We use trigonometry to find the components of the weight

sin 45 = Wₓ / W

cos 45 = W_{y} / W

Wₓ = W sin 45

W_{y} = W cos 45

The out of touch has the expression

fr = μ N

fr = μ W_{y}

We substitute in 1

μ mg cos 45 - mg sin 45 = m a

W_{y} = (a + g sin 45) / g cos 45

μ = a / g cos 45 + 1

We calculate

Acceleration goes down the plane, so it is negative

a = -4 m / s²

μ = 1- 4 / (9.8 cos 45)

μ = 0.423

Answer 2

Answer:

Answer:

The μ = 0.422

Explanation:

The distance travelled by the mass is equal to:

$L=ut+(1)/(2)at^(2) \n0.5=(0*5)+(1)/(2) a(0.5^(2) )\na=4m/s^(2)$

The sum of forces in y-direction equals zero:

∑Fy = 0

N - (m * g * cosθ) = 0

N - (1 * 9.8 * cos45) = 0

N = 6.93 N

The sum of forces in x-direction is equal to:

∑Fx = ma

(m * g * sinθ) - fk = m * a

(1 * 9.8 * sin45) - fk = 1 * 4

fk = 2.93 N

fk = μ * N

2.93 = μ * 6.93

μ = 0.422

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In the process of changing a flat tire, a motorist uses a hydraulic jack. She begins by applying a force of 48 N to the input piston, which has a radius r1. As a result, the output plunger, which has a radius r2, applies a force to the car. The ratio r2/r1 has a value of 9.0. Ignore the height difference between the input piston and output plunger and determine the force that the output plunger applies to the car.

Answers

Answer:

Force that the output plunger applies to the car; F2 = 3888N

Explanation:

For a hydraulic device, the relationship between the force and the area using Pascal's principle is;

F1/A1 = F2/A2

Where;

F1 is force applied to the input piston

F2 is force that the output plunger applies to the car

A1 is Area of input piston

A2 is area of larger piston

We are given;

R2/R1 = 9

So,R2 = 9R1

F1 = 48N

Area of input piston;

A1 = π(R1)²

Area of output piston;

A2 = π(9R1)²

Since, (F1/A1) = (F2/A2)

Thus;

F1/(π(R1)²) = F2/(π(9R1)²)

If we simplify, π(R1)² will cancel out to give;

F1 = F2/9²

Thus;

F2 = 9² x F1

Plugging in 48N for F1, we have;

F2 = 9² x 48

F2 = 81 x 48

F2 = 3888N

Final answer:

Using the principle of Pascal's law and ignoring the height difference, the output force is found by the formula F2 = F1*(r2/r1)^2. Given F1 is 48N and r2/r1 is 9.0, the output force F2 equates to 3888N.

Explanation:

In the case of a hydraulic jack, the principle of Pascal's law is applied. According to this law, pressure applied at one point of the fluid is transmitted equally in all directions. Therefore, if we ignore the height difference between pistons, the pressure exerted on both pistons would be the same.

Pressure is equal to the force divided by the area, where area equals π times the radius squared (π*r^2). So, the pressure at the input piston (P1) is the force at the input piston (F1) divided by its area (A1): P1 = F1/A1, where A1 = π*(r1)^2.

For the output plunger(P2 = F2/A2), where F2 = force at the output plunger and A2 = π*(r2)^2. By equating the pressures (P1=P2) and simplifying, we find that F2 = F1*(r2/r1)^2, where r2/r1 is given as 9.0. So, the output force F2 would be 48N*(9.0)^2 = 3888N.

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What is the meaning of relative as a noun?

Answers

Answer:

noun. a person who is connected with another or others by blood or marriage. something having, or standing in, some relation or connection to something else. something dependent upon external conditions for its specific nature, size, etc. (opposed to absolute).

A swimmer heads directly across a river, swimming at 1.00 m/s relative to still water. He arrives at a point 41.0 m downstream from the point directly across the river, which is 73.0 m wide. What is the speed of the river current?

Answers

Answer:

velocity of the river is equal to 0.56 m/s

Explanation:

given,

velocity of swimmer w.r.t still water = 1 m/s

width of river = 73 m

he arrives to the point = 41 m

$times = (distance)/(speed)$

$times = (73)/(1)$

t = 73 s

$velocity = (distance)/(time)$

= $(41)/(73)$

= 0.56 m/s

velocity of the river is equal to 0.56 m/s

A particle (q = 5.0 nC, m = 3.0 μg) moves in a region where the magnetic field has components Bx = 2.0 mT, By = 3.0 mT, and Bz = −4.0 mT. At an instant when the speed of the particle is 5.0 km/s and the direction of its velocity is 120° relative to the magnetic field, what is the magnitude of the acceleration of the particle in m/s2?

Answers

The acceleration of the particle is 38.87 kg.

Net magnetic field

The net magnetic field is calculated as follows;

$B_(net) = √(B_x^2 + B_y^2 + B_z^2) \n\nB_(net) = √(2^2 + 3^2 + 4^2) = 5.385 \ mT$

Magnetic force on the charge

The magnetic force on the charge is calculated as follows;

$F = qvB * sin(\theta)\n\nF = 5* 10^(-9) * 5* 10^3 * 5.385 * 10^(-3) * sin(120)\n\nF = 1.166 * 10^(-7) \ N$

Acceleration of the particle

The acceleration of the particle is calculated as follows;

$a = (F)/(m) \n\na = (1.166 * 10^(-7))/(3 * 10^(-9)) \n\na = 38.87 \ kg$

Learn more about magnetic force here: brainly.com/question/13277365

Explanation:

It is given that,

Charge on the particle, $q=5\ nC=5* 10^(-9)\ C$

Mass of the particle, $m=3\ \mu g=3* 10^(-6)\ g=3* 10^(-9)\ kg$

Magnetic field component, $B_x=2\ mT,B_y=3\ mT,B_z=-4\ mT$

Net magnetic field, $B=√(2^2+3^2+4^2)=5.38\ mT=0.00538\ T$

Speed of the particle, v = 5 km/s = 5000 m/s

Angle between velocity and magnetic field, $\theta=120$

Magnetic force is given by :

$F=qvB\ sin\theta$

$F=5* 10^(-9)* 5000\ m/s* 0.00538* sin(120)$

$F=1.16* 10^(-7)\ N$

Acceleration of the particle is given by, $a=(F)/(m)$

$a=(1.16* 10^(-7)\ N)/(3* 10^(-9)\ kg)$

$a=38.6\ m/s^2$

So, the acceleration of the particle is 38.6 m/s². Hence, this is the required solution.

If R = 12 cm, M = 430 g, and m = 60 g , find the speed of the block after it has descended 50 cm starting from rest. Solve the problem using energy conservation principles. (Treat the pulley as a uniform disk.)