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Dahasolnce [82]
3 years ago
12

Consider an eraser, weighing 20g, sitting 5cm from the center of a turntable (flat disk attached to a motor which can spin the d

isk up or down). If the coefficient of static friction between the eraser and the turntable is 0.1, and the turntable is slowly spun-up just shy of the spin rate at which the eraser starts to slip
A.Calculate how many revolutions the turntable will make every minute at the end (when the eraser is just about to slip). Show your reasoning!
B.What force is responsible for making the eraser go faster while the turntable is spinning up?
Physics
1 answer:
Artist 52 [7]3 years ago
7 0

Answer:

A. 42.3 revolution per minute

B. Centripetal Force

Explanation:

20 g = 0.02 kg

5 cm = 0.05 m

Let g = 9.8 m/s2

A.The friction force acting on the eraser is the product of normal force and its coefficient:

F_f = N\mu = mg\mu = 0.02*9.8*0.1 = 0.0196 N

For the eraser to begin slipping, its centripetal acceleration must win over the acceleration created by friction force, which is

a_f = F_f / m = 0.0196 / 0.02 = 0.98 m/s^2 = a_c

We can calculate the angular velocity from this:

a_c = \omega^2 r

where r = 0.05 is the radius of rotation, which is distance from the center to the eraser

\omega^2 = a_c/r = 0.98 / 0.05 = 19.6

\omega = \sqrt{19.6} = 4.43 rad/s

If it spins and angle of 4.43 rad per second then for every minute (60 seconds) it would spin an angle of 4.43 * 60 = 265.6 rad/min

Since 1 revolution is 2π rad, then in a minute it would spin 265.6 / 2π = 42.3 revolution/minute

B. The force responsible for making the eraser go faster while the turntable is spinning up would be the centripetal force.

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The electrostatic potential energy, U, of one point charge q at position d in the presence of an electric field E is defined as the negative of the work W done by the electrostatic force to bring it from the reference position d to that position

u \:  =  \:  \frac{kq1q2}{d}

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Which of the following is MOST useful to scientists in measuring the size of asteroids?
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Answer:c-The gravitational effect when spacecraft flies close to the asteriod

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5 0
2 years ago
the equation of motion is given for a particle when s is in meters and t is in seconds. Find the acceleration after 4.5 seconds
ki77a [65]

Answer:

Explanation:

The question is incomplete.

The equation of motion is given for a particle, where s is in meters and t is in seconds. Find the acceleration after 4.5 seconds.

s= sin2(pi)t

Acceleration = d²S/dt²

dS/dt = 2πcos2πt

d²S/dt² = -4π²sin2πt

A(t) = -4π²sin2πt

Next is to find acceleration after 4.5 seconds

A(4.5) = -4π²sin2π(4.5)

A(4.5) = -4π²sin9π

A(4.5) = -4π²sin1620

A(4.5) = -4π²(0)

A(4.5) = 0m/s²

4 0
2 years ago
A steel drill making 180 rpm is used to drill a hole in a block of steel. The mass of the steel block and the drill is 180 g. If
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Answer:

a) 37.8 W

b) 2 Nm

Explanation:

180 g = 0.18 kg

We can also convert 180 revolution per minute to standard angular velocity unit knowing that each revolution is 2π and 1 minute equals to 60 seconds

180 rpm = 180*2π/60 = 18.85 rad/s

We can use the heat specific equation to find the rate of heat exchange of the steel drill and block:

\dot{E} = mc\Delta \dot{t} = 0.18*420*0.5 = 37.8 J/s

Since the entire mechanical work is used up in producing heat, we can conclude that the rate of work is also 37.8 J/s, or 37.8 W

The torque T required to drill can be calculated using the work equation

E = T\theta

\dot{E} = T\dot{\theta} = T\omega

T = \frac{\dot{E}}{\omega} = \frac{37.8}{18.85} = 2 Nm

7 0
3 years ago
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