A frictionless plane is 10.0 m long and inclined at 33.0°. A sled starts at the bottom with an initial speed of 4.30 m/s up the incline. When the sled reaches the point at which it momentarily stops, a second sled is released from the top of the incline with an initial speed vi. Both sleds reach the bottom of the incline at the same moment.
(a) Determine the distance that the first sled traveled up the incline.
1 m
(b) Determine the initial speed of the second sled.
2 m/s
Hint: Active Figure 4.21
To solve this problem, we can use the principles of conservation of energy and the equations of motion.
(a) To find the distance that the first sled traveled up the incline, we need to determine the height it reached before momentarily stopping. We can use the conservation of energy principle:
Initial kinetic energy + Initial potential energy = Final kinetic energy + Final potential energy
Since the sled starts from rest, the initial kinetic energy is zero. The initial potential energy is given by mgh, where m is the mass of the sled, g is the acceleration due to gravity, and h is the height reached by the sled.
The final kinetic energy is also zero since the sled momentarily stops. The final potential energy is also given by mgh, where h is the height reached by the sled.
Setting these two equations equal, we can solve for the height h:
0 + mgh = 0 + mgh
mgh = mgh
Canceling out the mass, we get:
h = h
This means that the height reached by the sled is the same as the initial height of the sled, which is the height of the inclined plane. The inclined plane is 10.0 m long, and at an angle of 33.0°. To find the vertical height h, we can use the equation:
h = length of inclined plane * sin(angle)
h = 10.0 m * sin(33.0°)
h ≈ 5.42 m
Therefore, the distance that the first sled traveled up the incline is approximately 5.42 m.
(b) To determine the initial speed of the second sled, we can use the equations of motion. The first sled reaches the bottom of the incline with zero speed, so its final kinetic energy is zero. The second sled starts from the top of the incline and reaches the bottom with non-zero speed.
Using the equation of motion:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled.
Since the sled starts from rest at the top of the incline, its initial velocity is zero. The acceleration can be determined using the component of gravity along the incline, which is given by:
acceleration = g * sin(angle)
acceleration = 9.8 m/s^2 * sin(33.0°)
acceleration ≈ 5.38 m/s^2
The distance traveled by the second sled is the length of the incline, which is 10.0 m.
Plugging in these values into the equation of motion, we can solve for the final velocity:
v^2 = 0^2 + 2 * 5.38 m/s^2 * 10.0 m
v^2 = 107.6 m^2/s^2
Taking the square root of both sides:
v ≈ 10.4 m/s
Therefore, the initial speed of the second sled is approximately 10.4 m/s.
Answer:
(a) The distance that the first sled traveled up the incline is approximately 5.42 m.
(b) The initial speed of the second sled is approximately 10.4 m/s.
a) mgh=1/2 m v^2
distance up slide=h/sin33
gdsin33=v^2
d= 4.3^2/(9.8*sin33)=
I don't get your answer.
b) I will be happy to critique your thinking.