Answer:
1.10 m/s
Explanation:
Linear speed is given by
Kinetic energy is given by
Potential energy
PE= mgh
From the law of conservation of energy, KE=PE hence
where m is mass, I is moment of inertia,
is angular velocity, g is acceleration due to gravity and h is height
Substituting m2-m1 for m and 0.5l for h,
for
we obtain
and making v the subject
For the rod, moment of inertia
and for sphere
hence substituting 0.5L for R then
For the sphere on the left hand side, moment of inertia I
while for the sphere on right hand side,
The total moment of inertia is therefore given by adding
Substituting
for I in the equation
Then we obtain
This is the expression of linear speed. Substituting values given we get
The ball has an initial speed of 10m/s. This is because it is moving with the balloon. Now the balloonist throws the ball 4m/s with respect to himself, so it means that he gives the ball a extra push of 4m/s, so the total speed is 14m/s. Since it takes 30 seconds to reach the ground, the distance travelled is 14*30=420m.
Answer:
4.9 cm
Explanation:
From Hook's Law,
F = ke......................... Equation 1
Where F= force, e = extension, k = spring constant.
Note: the Force acting on the the spring is the weight of the mass.
W = mg.
F = mg.................... Equation 2
Where m = mass, g = acceleration due to gravity
Substitute equation 2 into equation 1
mg = ke
make e the subject of the equation
e = mg/k............... Equation 3.
Given: m = 2 kg, g = 9.8 m/s², k = 400 N/m
e = (2×9.8)/400
e = 19.6/400
e = 0.049 m
e = 4.9 cm
During the fall, the potential energy stored in the ball is converted into kinetic energy.
Thus,
PE = KE before hitting the ground
= 1/2 • mv^2
= 1/2 • 1 • 12^2
= 72J