Answer:
(a) W = 8.66 J
(b) Velocity = 2.40 m/s
Explanation:
(a) Work done is given as the product of force and displacement. That is:
W = F * d * cos(A)
Where F = force applied
d = distance moved
A = angle of ramp
Therefore, work done is:
W = 20 * 0.5 * cos30
W = 8.66 J
(b) Work done is equal to change in Kinetic energy. Since the initial kinetic energy is zero:
W = KE(final)
W = ½ * m * v²
Where v = final velocity
=> 8.66 = ½ * 3 * v²
v² = 5.773
v² = 2.40 m/s
Answer:

Explanation:
Let's start by writing the equations of the forces along the two directions:
- Vertical:

where
N is the normal reaction
is the angle between the road and the horizontal
(mg) is the weight of the car, with m being its mass and g the acceleration of gravity
- Horizontal:

where
v is the speed of the car
r is the radius of the turn
Dividing the 2nd equation by the 1st one, we get:

In this problem:
(radius of the turn)
is the speed

Substituting, we find:

Answer:

Explanation:
The frequency of a simple pendulum is given by:

where
g is the acceleration of gravity
L is the length of the pendulum
Calling
the length of the first pendulum and
the acceleration of gravity at the location of the first pendulum, the frequency of the first pendulum is

The length of the second pendulum is 0.4 times the length of the first pendulum, so

while the acceleration of gravity experienced by the second pendulum is 0.9 times the acceleration of gravity experienced by the first pendulum, so

So the frequency of the second pendulum is

Therefore the ratio between the two frequencies is
