For the mass m, attached to a spring, to move in a circle centripetal force and restoring force of the spring must be equal. Centripetal force is given with this formula:
Restoring force only occurs if the spring is stretched. If L is the length of unstretched spring we have the following formula for restoring force:
r is the length of a circle that mass m is traveling along.
As said above, these two forces have to be equal:
We solve for r:
r(w) will go to infinity when denominator is equal to zero:
Please keep in mind that Hooke's law has it's limitations, and before we reach our critial value of angular velocity spring will be strecthed to a point where Hooke's law does not aply anymore.
Answer:
Explanation:
The period of a simple pendulum is given by the equation
where
L is the lenght of the pendulum
g is the acceleration due to gravity at the location of the pendulum
We notice from the formula that the period of a pendulum does not depend on the mass of the system
In this problem:
-The pendulum comes back to the point of release exactly 2.4 seconds after the release. --> this means that the period of the pendulum is
T = 2.4 s
- The length of the pendulum is
L = 1.3 m
Re-arranging the equation for g, we can find the acceleration due to gravity on the planet:
Answer:
Explanation:
Given:
- mass of aluminium,
- initial temperature of the aluminium cylinder,
- mass of coffee,
- initial temperature of coffee,
- specific heat of coffee (assuming water),
- specific heat of aluminium,
When the coffee and the aluminium cylinder come in contact then heat released by the coffee is equal to the heat gained by the aluminium.
<u>Mathematically:</u>
is the final temperature of agreement.
Answer:
C
Explanation:
The mechanical advantage is always less than 1 because the force needed to move an object is always greater than the weight of the object.
Answer:
the speed of the block at the given position is 21.33 m/s.
Explanation:
Given;
spring constant, k = 3500 N/m
mass of the block, m = 4 kg
extension of the spring, x = 0.2 m
initial velocity of the block, u = 0
displacement of the block, d =1.3 m
The force applied to the block by the spring is calculated as;
F = ma = kx
where;
a is the acceleration of the block
The final velocity of the block at 1.3 m is calculated as;
v² = u² + 2ad
v² = 0 + 2ad
v² = 2ad
v = √2ad
v = √(2 x 175 x 1.3)
v = 21.33 m/s
Therefore, the speed of the block at the given position is 21.33 m/s.