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kirza4 [7]
2 years ago
10

A 5.50 kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force F(t) is applied to the en

d of the rope, and the height of the crate above its initial position is given by y(t) =(2.80 m/s)t +(0.61 m/s^3)t^3.
Required:
a. What is the magnitude of the force F when 4.10s ?
b. Is the magnitude's unit N but the system doesn't accept it?
Physics
1 answer:
11Alexandr11 [23.1K]2 years ago
8 0

Answer:

Explanation:

position

y(t) = 2.80t + 0.61t³

velocity is the derivative of position

v(t) = 2.80 + 1.83t²

acceleration is the derivative of velocity

a(t) = 3.66t

F = ma = 5.50(3.66(4.10)) = 82.533 N

which should be rounded to no more than three significant digits and arguably only two due to the 0.61 factor.

F = 82.5 N or 83 N

Yes the units are Newtons, cannot tell what your system will accept. May not want the units at all.

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3 years ago
A Ferris wheel turns at a constant 150.0 revolutions per hour. (a) Express this rate of rotation in units of radians per second.
RUDIKE [14]

Answer:

(a) 0.261 rad/s

(b) 1007.72 m

Explanation:

The angular velocity of the Ferris wheel is 150.0 revolutions per hour.

(a) To calculate the angular velocity of the wheel in units of radians per second, you take into account the following equivalence:

1 hour = 3600 seconds

1 revolution = 2π radians

You use the previous conversion factors:

150.0\ \frac{rev}{h}*\frac{2\pi \ rad}{1\ rev}*\frac{1\ h}{3600\ s}=0.261\frac{rad}{s}

In units of radians per seconds the wheel turns at 0.261 rad/s

(b) To find the arc length described by the wheel, you first calculate the angle described by the  wheel in the time t, by using the following formula:

\theta=\omega t     (1)

ω: angular velocity = 0.261 rad/s

t: time = 4.95 min

You first convert the time to units of seconds

4.95min*\frac{60s}{1min}=297s

Next, you replace the values of the parameters in the equation (1):

\theta=(0.261\frac{rad}{s})(297s)=77.51rad

Next, you use the following formula for the arc length:

s=r\theta     (2)

r: radius of the wheel = 13.0 m

You replace the values of the parameters in the equation (2):

s=(13.0m)(77.51rad)=1007.72m

The arc length described by the wheel is 1007.72m

4 0
3 years ago
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