> A
carousel is moving with uniform circular motion. The centripetal acceleration
of the ride is:
Centripetal acceleration is always directed toward the center of motion
> Where should a force be applied on a lever arm to
produce the most torque?
farthest from the axis of rotation
> A boy can raise a rock that weighs 120 N by using a
lever and applying a force of 25 N.
What is the mechanical advantage of the lever?
Simply divide the weight by the force applied:
120 / 25 = 4.8
> A pebble that is 3.81 m from the eye of a tornado
has a tangential speed of 124 m/s. What is the magnitude of the pebble's centripetal
acceleration?
Centripetal acceleration is calculated using the formula:
a = v^2 / r
a = (124 m/s)^2 / 3.81 m
a = 4,035.70 m/s^2 ~ 4036
> A dog sits 1.25 m from the center of a merry go
round and revolves at a tangential speed of 2.0 m/s. If the dog's mass is 19.3
kg, what is the magnitude of the centripetal force on the dog?
a = v^2 / r
a = (2.0 m/s)^2 / 1.25 m
a = 3.2 m/s^2
The force is:
F = m a
F = 19.3 kg * 3.2 m/s^2
F = 61.8 N
> A ball attached to a string is whirled in a circle.
If the string breaks, what causes the ball to move in a straight line?
The force which is directed away from the center of the
motion: centrifugal force
> Find the magnitude of the gravitational force
exerted on a 66.5 kg astronaut on the surface of Planet X if the planet has a
radius of 4.40 x 10⁶ m and a mass of 8.43 x 10²³ kg.(Use G= 6.67 x 10⁻¹¹
Nm/kg²)
We use the formula:
F = G m1 m2 / r^2
F = 6.67 x 10⁻¹¹ Nm/kg² * (66.5 kg) * (8.43 x 10²³ kg) / (4.40
x 10⁶ m)^2
F = 193 N
> How would the speed of the Earth's orbit change if
the Earth's distance from the Sun increased by 9 times?
The orbital speed is related to distance from the
formula:
v = sqrt (GM / r)
where r is the distance from Earth to Sun
so if r’ = 9 r
v = sqrt (GM / 9r)
v = (1/3) sqrt (GM / r)
Therefore: Decrease by a factor of 3
> What is the efficiency of a crane that requires
28,000 J of energy to lift a 200 kg object 10 meters?
The total work done is:
Work = 200 kg * 9.8 m/s^2 * 10 m
Work = 19,600 J
So efficiency is:
efficiency = 19,600 / 28,000 * 100% = 70%
> What is the force required to produce a 1.4 Nm
torque when applied to a door at a 60.0º angle and 0.40 m from the hinge?
The perpendicular component of the applied force is:
F * sin(60°) = 0.866F N
Since the moment arm is 0.40 m, the torque is:
(0.866F N)*(0.4 m) = 0.3464F N-m
This torque is equal to a value of 1.4 N-m, therefore
0.3464F = 1.4
F = 4.0 N
